Many thanks to many posters for contributing their suggestions and past reports. We relied on them and on guidebook recommendations, chiefly Fred Plotkin's Italy for the Gourmet Traveller, but others as well.
DONNA TERESA, via Kerbaker (the Vomero district)
Although my husband had never read a single review or recommendation for this restaurant, he said blissfully after a few bites of his first course: "This is the kind of restaurant you dream of finding in Italy and think you never will." As we were leaving -- having made a reservation to return the next night -- he said to me: "Best meal of the year." (This after 15 restaurant dinners in Bologna.) During our six nights in Napoli, we dinner ate at Donna Teresa three times -- and loved every meal. (My second night there, I found myself suddenly thinking: "I wish I could cook like this!" And I wish I thought that more often in Italian restaurants of great renown.) We would have eaten at Donna Teresa all six nights of our stay had not they been closed for one, had not our landlady offered to make us a home-cooked pasta alla genovese -- an offer impossible to refuse -- and had we not felt obliged to give Neopolitan pizza another try.
It is probably easy to oversell this restaurant to people expecting something other than what it is -- simply a wonderful dinner and a warm experience. What is offered is so seasonal it seems beside the point to say what we ate, but I will. A white bean and escarole soup, a ziti-like pasta with eggplant and provolone cheese (one night tossed in a light tomato sauce, another night baked). For meats we had sausage, pork in a ragu, One night we had octopus cooked in tomato and wine. Every night, we had a tasty array of seasonal local vegetables, cooked perfectly. For desserts we had (on different nights) struffoli, pastiera and clementines. The wine came in an unlabeled bottle. It was red and it was good, and we were given one glass to drink it with, the same glass we were given to drink our water. Table cloths are plastic. Napkins are paper. Our 3 course meals, with wine, were 13 euros per person.
Although Donna Teresa is now recommended by many, it was Fred Plotkin's description of his dining experience there that led me to it (and the entire district of Vomero) and so I feel a special debt of thanks for having had such a good time following his advice.
THE SINGING WOMAN SELLING STEAMING BREAD OUT OF A BABY CARRIAGE (vico San Domenico Maggiore, centro storico)
As my husband and I were walking pretty much by ourselves through the centro storico, a solitary woman coming from far in the opposite direction, dressed entirely in pink and pushing a baby carriage, was sing-songing out, repeatedly, something we couldn't quite catch -- but suddenly several people popped out of doorways to flag her down, digging into their pockets for change. She reached under the covers of her baby carriage and pulled out many steaming rounds of soft bread, the size of plump saucers, wrapped in paper towels, passing them around and getting money in return. When I stepped in closer for a look, another Neapolitan woman urged me to buy one, drilling her index finger into her cheek and rolling her eyes in delight. So we bought a fat. steaming round of bread for 2 euros, and when we bit into it, it was filled with a juicy pork stew and a hard-boiled egg. A few moments later, there was a huge thunderclap, and it began to hail like crazy. When ducked into a doorway, and when we looked again, the woman pushing the baby carriage had vanished, although we could still hear her singing. We are certain we did not dream her, and if we ever found her again, we would buy another round of steaming stuffed bread from her. It was better than all the pizze and sfogliatelle we ate in Napoli.
DON SALVATORE, via Mergellina (Mergellina seafront)
Luciano Pignataro' s description of this Neapolitan quasi-institution made it my choicefor a big fishy and fancy Sunday lunch, and we were not disappointed in our choice, especially for the freshness of the ingredients, the heirloom recipes and the warm ambience (we were surrounded by huge happy families who had just come from baby christenings). Best of the meal was antipasto of frutti di mare, a spaghetti al vongole (studded with incredibly tasty cherry tomatoes), an excellent seafood risotto, and mazzancolle steamed and dressed with a chickpea puree, which I found exquisite. We drank Greco di Tufo, and didn't eat dessert. Something around 50e per person.
MIMI ALLA FERROVIA, via Alfonso d'Aragona (just off Piazza Garibaldi)
I had eaten here before (following Fred Plotkin's lead) and while I enjoyed the space, I felt I had ordered poorly, so I wanted to give it another try. I wasn't sorry. We started out with escarole stuffed with anchovies, pine nuts, capers and olives (and a bit of bread), and it was just perfect. We followed with a schiaffoni (pasta) with frutti di mare, and it was very tasty indeed. We drank the house white, no dessert. About 20e per person.
LA CANTINA DI SICA, via Bernini (Vomero)
We went in on a whim and had a first-class whole fish (spigola) baked in salt, along with a simple octopus salad that had the bright taste of lemon and seawater, and a tasty pasta (sedanini) with squid and deep green olives. We split the house dessert -- a kind of high-end cassata with a chocolate sauce. We asked for a greco di tufa and inexplicably ended up with a white we liked less. The high vaulted-ceiling restaurant with deep red walls is hushed and calming, and a 1951 Toto movie played (silently) the whole time we were there on a rear wall, making us laugh. Dinner about 35e pp.
GORIZIA, via Albini (Vomero)
Pizzeria Gorizia has two locations in Vomero. We ate at the one closest to where we were staying (not the one closest to the funicular stops). Gorizia rated an extended entry in Luciano Pignataro's blog (and a mention inFred Plotkin's book). Before tucking into our marinara pizze, we really enjoyed sampling the house friarelli (broccoli rabe), cooked to a fare thee well. Our pizze was quite pretty to look at, smelled great and -- well, either Neapolitan pizza is your kind of pizza or it ain't! (I prefer Roman pizza, although I recognize that Neapolitan pizza is a great culinary invention, believe me). We drank a Tuscan novello. Meal was about 12e pp.
CIRO a SANTA BRIGIDA, via Santa Brigida (near Galleria Umberto I)
I had heard that non-Italians don't always get such a warm welcome, but we were treated splendidly, ushered to a table on glassed-in balcony that enabled us to watch the Neapolitan street theater below. I had picked the restaurant (recommended by Plotkin) because I wanted to try its version of pasta alla genovese -- and at the last minute I bailed and joined my husband in ordering pizza, this time with mozzerella. The cheese was pleasantly salty and I liked their crust more than I liked Gorizia's (Ciro's was chewier), but in the end, I wasn't thrilled to be eating another pizza. (Yeah, weird, I know). An antipasta of sauteed clams was very nice. No dessert. House white. Probably 25e per person, and we enjoyed ourselves overall.
LA CANTINA DI VIA SAPIENZA, via delle Sapienza (centro storico)
This was recommended by one of the guidebooks I was using (I can't remember now whether it was the Italian Touring Club or the Rough Guide), and Katie Parla has it on her list. A pasta with mushrooms was very pleasant as was an assortment vegetables and the house red. No dessert. Meal was about 15e per person. Most enjoyable was the down home ambience.
SOAVE, via A. Scarlatti, Vomero
This is mainly a gelateria, but they also have a deli in the back, where we purchased got a picnic lunch of very tasty Neapolitan salami, chewy bread and delicious smoked provolone (the last of which we shared with a half-dozen extremely well-behaved dogs of Pompei).
OTHER TREATS, DRINKS, ETC.
CAFE MEXICO was by far the best coffee we drank (it has multiple locations). I enjoyed my miniature baba au rhum from MIGNONE (in Piazza Cavour) but nothing else I ate there (including its sfogliatelle). Perhaps simply by virtue of being warm, the sfogliatelle at ATTANASEO (near Pizza Garibaldi) was the best I tasted, although I still could have cared less. I disliked everything about SFOGLIATELLE MARY, including its baba and its sfogliatelle. Rabarbaro Zucca isn't Neapolitan, but you can get it served warm at CAFFETTERIA VANVITELLI (piazza Vanvitelli), a great place to watch the passing scene in a very lively part of town, especially during the Christmas shopping season. The staff is very friendly.
HOME COOKED PASTA ALLA GENOVESE AND WINE WITH THE FEET
I quite innocently asked the landlady at the apartment where I was staying if she could recommend a restaurant for good pasta alla genovese -- and instantly but belatedly realized she would insist on cooking it for me herself. I tried every way to dissuade her from going to the trouble. She wouldn't hear of it. It was wonderful to taste her down home version -- I suspect no two could ever be alike. She stressed the importance of using local onions (of course!), because she insisted the dish should be slightly bitter, an impossibility if you use sweet onions. She also cautioned me to finish the pasta in the pan. The meat from the sauce served as the secondi was particularly moist and tender (mine usually dries out).
To drink, she offered us a choice of a bottle of red wine and a carafe of red wine -- the latter which she warned us of was made "with the feet" lest we be squeamish -- but very clean feet she emphasized. We of course wanted the wine with the feet, which was light, dry and refreshing.
She also baked for us her own pastiera, which was pleasant for being less sweet most every other version I tasted. We had that for breakfast.
As enjoyable as the food was her conversation, about the history of Naples, her travels around the world, her life story, in a wonderful home stuffed with family treasures, and a view of the port and Capri.