First, of course, I have to thank all the previous posters here about Sicily - though they're sometimes few and far between (especially recently), Chowhound recommendations are always still the best - better than Slowfood, better than Plotkin, better than Gambero Rosso, definitely better than Michelin, just the best. So thanks!
Second, just a general observation from our time spent in Sicily - if you're planning a trip and you want to visit the beautiful (and touristy) places like Taormina and Siracusa, don't fret that there won't be any good food for you there, or think that it's all in Palermo so you HAVE to make a stop there. We actually found the opposite to be true from our small sampling.
PALERMO (and nearby-ish)
While not the high point, we did have some nice meals here, especially on day trips. And the Arab-Norman architecture is reason enough to go, even if you just spent all your meals in your apartment cooking goodies from the markets (which don't disappoint).
I would recommend:
Monte San Giuliano in Erice (for great smoked fish, a dish of ravioli di ricotta con seppia where the inky sauce was just full of flavor, crespelle with broccoli and spiced couscous with fish; abbondanza was the rule here, as both the ravioli and crespelle were ceremoniously topped with a pretty ridiculous amount of ricotta tableside - they already both were filled with the stuff, plus bechamel in the crespelle - but we'd had such a lousy rainy day that the over-the-top lunch was just what we needed)
Trattoria del Pavone in Monreale (for their wine list, antipasti, polpette di sarde, and tortelloni di vitello in a curry sauce of all things - which was especially nice with the bits of eggplant they added in; this place was an elegant escape from the crowds at the cathedral)
We also visited a few other places in Palermo that had some high and low points:
Basile (really simple, giant plates of pasta/antipasti, one of the cheapest meals I have ever had in Europe, very friendly service; my pasta al sugo di salsiccia was enjoyable, but my BF's ravioli was sadly cold and boring, so its a roll of the dice)
Antica Foccaceria San Francesco (the milza is definitely worth getting - totally greasy comfort food, elevated by the bread and cheese; also tried their arancino alla norma which was fine but not outstanding; we actually ate in the ristorante upstairs, which had a lovely view, but I don't think anything we ate up there was really so worthwhile - you're better off eating your street food style selections downstairs as those were the highlights)
Sant'Andrea (for the antipasto of pane fritto with bacalao and sweet caramelized onions; the primi and secondo we had didn't quite come together - they were trying some creative combinations that didn't work, but the space was pretty and service nice)
Osteria dei Vespri (voluminous wine list - so heavy it required its own chair(!); this is a tasting menu type place, with dainty, somewhat belabored food, most of which was just ok, standouts being a very homey gnocchetti with rabbit and a little taste of tuna tartare with superfresh flavorful herbs; our main of "lamb two ways" was sadly overcooked and bland)
Sfincione from a guy at Ballaro market (I can see the comparison to the NY grandma slice; a very enjoyable snack with simple flavors, and nice textural contrast between the spongy bread and crisp crust - but I wouldn't go out of my way to get it here, anywhere on the street is probably fine)
Spinnato (for their gelato in brioche - very enjoyable but not life changing)
And if I had it all to do over, I would have skipped:
Piccolo Napoli - really underwhelming
Pasticceria Maria Grammatica - had a cannolo that was just bad - they must be coasting on fame; I had a much better one later at an agriturismo
And instead visited:
Ai Cascinari - which was closed when we planned to visit
Markets of note:
We stayed right by the Capo market, which was great, perhaps a bit smaller than Ballaro, but I found it much more atmospheric and it had equally impressive produce and fish. I would recommend seeing whichever is closer to the rest of your itinerary; you don't need to do more than one.
Another note about Palermo - from the descriptions of others, we expected it to be crazy like Naples (where any moment it feels like you could be attacked by a pack of feral children on scooters - which to me is endearing - I love Naples), but it was just a very average Italian city, lots of middle class college students, working class folks, no real danger, friendly people, but also less personality than I expected. Certainly no need for anyone to worry about safety while visiting there. It felt just like walking about NY or any other large city.
I can see why the tourists love this little town. We stayed on Ortigia and it was just beyond charming - the perfect scale town to explore leisurely. If you like jogging, that is apparently THE thing to do here, so bring your trainers and soak up the views working off all that pasta.
I heartily recommend:
Oinos (for their creative Sicilian dishes - highly recommended here on CH, and I have to agree; we had the single best dish of the trip at Oinos: a not-remotely-Sicilian and possibly crazy-sounding cacio e peppe with lime marinated scampi crudo mixed in, which was so unbelievably good we came back a second night - but they were full! Also excellent was their fennel and orange salad with peppers and anchovies, grilled octopus, and their spaghetti ai ricci with summer squash on top of a bed of braised greens.)
Osteria Gazza Ladra (for their antipasti alla Siracusana - a bounty of perfect vegetable nibbles - plus a frittata, and simple, balanced pastas: one with just anchovies, breadcrumbs, ground almonds and oil, and other with a light local fish and parsley - they sound boring but were perfectly executed, and the proprietress so friendly, I'm surprised we didn't eat here more than once as well)
Caseificio Borderi (for sandwiches to go; this place was swamped so it took a while to get an order in but we were rewarded with two of the best sandwiches we've ever had, each just 2euro - one was just prosciutto with mozzarella and caponata, the other was a salsiccia of some kind with a firmer cacio-like cheese and a sicilian pesto; plus the folks there are super nice)
We had a pretty enjoyable, but not outstanding meal at:
Porta Marina (for their house specialty of spaghetti and shrimp with smoked swordfish and breadcrumbs in a really fantastic buttery rich sauce - it was more northern Italian tasting than Sicilian, but still a winner; the marinated crudo and the sformato of zucchini were both nice, as was the sea urchin sauce on the ravioli of scampi - though the scampi failed to make much of an impact)
And I would avoid the following:
Vite e Vitello (everything was lackluster - how is this place a Slow Food pick? - with the exception of our secondo, the caramela di orata, which was an exceptional piece of fish wrapped up like a giant piece of candy in puff pastry - by no means should you make a stop here just for this, but if you're dragged here, get this!)
Trattoria da Mariano (I know people like this place but yikes, it was PAINFUL. We, and another Italian couple next to us, sat there an hour without even getting our wine. I'm all for slow meals but jeez, no drinks even? Then the salad and antipasto arrived sometime during hour two, both were good enough but nothing special. One of our pastas was quite nice - one of the only spicy dishes we had in Sicily, just a simple pasta con frutti di mare, but the other pasta was a tasteless rendition of pasta al nero di seppie that we didn't finish despite being by this time rather hungry. Our main was an abysmal dish of lumache - horribly bitter and disappointing. We averaged one dish an hour and were there past midnight - so did several other annoyed tables. Unless you are here with a big group and really don't care how long the lags are between your courses - maybe you've brought your own wine? - this place is just not worth the effort.)
Trattoria Crocificio del Bagliere in Noto (for their tender roast octopus, a pretty epic lasagna with broccoli, sausage and bechamel, another great ravioli di ricotta al nero di seppie with perfectly cooked sepia, coniglio al agrodolce and a very good wine list - even at lunch they filled up, so book this one or arrive early; it's slightly elevated cooking in a pleasant, contemporary space, and was an excellent value)
Don't understand the raves:
Cafe Sicilia (granted I am not really a huge fan of sweets, but neither of the little cakes we had here were good - didn't finish them)
Dolceria Costanzo (we didn't find anything particularly outstanding about their gelato, but there wasn't anything wrong with it either)
Beware if you are taking the train from here, they weren't selling tickets at the train station (no machine, no human, no nothin - just a sign informing you the nearest place to get them is about 10-15 minutes away, up the hill).
I know people complain about Taormina being touristy, but at least in early May when we were there, the only touristy area was the main Corso, which was indeed awful, but easy to escape. Just a block or two off, and you're all by yourself in a truly lovely old town, with incredible views at every turn. Rent yourself a house or apartment nearby and just drink up the natural beauty in privacy - it's really unbeatable.
We had outstanding meals here too (though you will spend more), at:
L'arco dei Cappuccini (which has the online reputation of being the best restaurant in town, and I believe it - everything we had from start to finish was excellent, even the secondo, which we had not really been so impressed with at other places. From their special of whitebait pressed into patties and fried, to the classic pasta alla norma and pasta con le sarde - the best renditions of either dish we had on the trip - to the brilliant costoletta di vitello with Etna mushrooms, with the veal just seared, so tender and pink inside, there was not one misstep. Everything perfectly seasoned and balanced.)
Nero D'Avola (where they do an excellent job of bringing together all of the best local product, have a very deep and focused wine list full of great stuff, and were just generally very nice, welcoming folks. We loved their tuna tartare - every bite was different, first a perfect caper, then a crunch of sea salt, then a hit of ginger. Two different dishes of suino nero were also outstanding - one an intensely piggy fettucine with Nebrodi mountain sausage and local mushrooms; another a pile of thin slices of maialino, some belly, some loin, all browned in a pan, then layered with cheese and toast to soak up the drippings. And then one of the best surprises - a lemon salad with just red and green onions and salt - the lemons were so sweet you could eat them rind and all. This is the place to go for a showcase of top notch local Sicilian goods.)
Not quite in a class of those, but also very good were:
Al Duomo (for the view, the marinated anchovies in orange, the pasta alla vecchia Taormina and con le sarde - both very good, close rivals of those from L'Arco dei Cappuccini - and the excellent sarde a beccafica; the value equation here is the only black mark - smallish portions and somewhat high prices are the tradeoff for the charming view of the square)
Al Saraceno (for pizza - the one with crushed tomatoes, cherry tomatoes, smoked tuna, arugula, mozzarella and olive oil was a standout; and pretty good beef carpaccio, as well as the great view)
We had some hits and misses at:
Viccolo Stretto (for the over-the-top pasta which was a bit like a marriage of pasta con le sarde and a ragu bolognese, with both anchovies and ground pork in a rich tomato sauce with cream swirled around the outside - just because it wasn't already rich enough! Caution: this place is also pricey and some of the dishes too precious for my taste. Other dishes were cooked nicely but the seasoning was a bit off.)
Trattoria da Nino (the salad of smoked fish was fabulous, the tuna tartare nice, the pastas good but unremarkable, but the service was very welcoming and cheery)
And I don't think I would bother with:
Al Melograno (dishes lacked balance, some elements were overcooked, it wasn't all bad, but nothing really stand-out)
Agriturismo San Marco (where we stopped for a lunch break during a day of hiking on Etna - their antipasti spread was neverending, and all of it was delicious. Highlights were a head cheese made with lemon infused into the gelatin, fried cheeses, and many many vegetables. Their mini cannoli were also lovely - not too much sugar, just fresh ricotta cheese speckled with vanilla. Pastas and wine were forgettable, but the location and antipasti were worth a stop, and the price was very low.)
I also urge you, if you're in the area and have the means, to go out to visit some of the wineries on Etna - just find a wine you like and go! We spent a day doing just this, and had a wonderful time - and a wonderful meal - in the process. We visited Frank Cornelissen and Salvo Foti on the North side of Etna, both of whom make incredible wines and were charming hosts. Or maybe I should say that Signore Foti's wife is the charming hostess, since her lunch was just delightful - most of it straight out of their pizza oven (I am so jealous of this lifestyle). Her artichokes made it hard to drag my sad self back to the Catania airport and real life this side of the pond. That's probably an exaggeration; it had something to do with the mountain views and the wine as well!