Just returned from a weeklong trip to Istanbul. Visited in April 2008 and was able to hit some old favorites and make some new ones. We stayed in the Beyoglu and Taksim areas which I find much better for food options in general than in Sultanhamet. Many of the new spots we tried were culled from IstanbulEats.com
çukur Meyhane - located just off Istiklal Caddesi almost directly across from the Flower Passage featuring homestyle mezes. Ate here twice for dinner, reservations recommended otherwise eat early (6 or 7pm). Favorite dishes include the fish ravioli (manti) which were lightly fried cubes of fish/spices/breadcrumbs (?) in a yogurt sauce, eggplant in sauce (chunky cold stewed eggplant with tomato), pepper puree (classic Turkish spread), cretan puree (bright springy taste, greens, herbs, and a farmers cheese), grilled halloumi, thin sliced pan fried liver (with pickled cabbage and carrots) if you are a big liver fan. Fairly inexpensive meal, was a favorite
Farrooj al Zaeem - 24 hour Syrian fast food chain also a few blocks off the top end of Istiklal Caddesi. No reservations needed, very inexpensive. Recommend the chicken durum wrap (tavuk durum) with garlicky mayo and a less spicy red sauce like hot sauce. Great creamy hummus as well topped with whole chickpeas. One durum + hummus is enough for 2 people to share.
Sıdıka Meze Restoranı - a little further out in the Beşiktaş neighborhood, walkable if you are on the far outskirts of Taksim. Reservations needed. Modern mezes (updated, not fancy) Pistachio and feta spread, dilly fava puree, char grilled octopus recommended
Kara Mehmet Kebap Salonu - If you're shopping at the Grand Bazaar and get hungry, this is your spot. Tender and juicy Adana kebab was a clear winner. This spot is a bit hard to find in the far right corner of the Cebeci Han courtyard, up an alley off of one of the bazaar's aisles.
Took the bus out to Rumeli Fort for breakfast at Kale Cafe (featured on No Reservations) for what looked like an amazing breakfast spread. It was pretty good but if I were to do it again would probably stay local to the Beyoglu area and give Van Kahvaltı Evi a shot.
Karakoy Gulluoglu - The best baklava. Love the Sutlu (rich, no nuts) baklava for something a little different. I always bring back a box or two as my food souvenir.
For dried fruits and cheeses, there is a really great market street on the Asian side, Güneşli Bahçe, that has a number of shops similar to what you'd find in the Spice Bazaar with much less hassle. Picked up amazing dried apricots at Brezilya Kurukahve along with some great fruit leather triangles studded and filled with hazelnuts. Ciya and Eta Bal honey shop are also located on this street. There is a large supermarket as well for buying packets of spices cheaply as well as interesting varieties of candy bars, chips, fruit molasses etc. This street is 3 blocks inland from the Kadikoy ferry station.
My favorite snack is the mussles stuffed with spiced rice most easily found at the fish vendor stalls off Istiklal Caddesi next to the Flower Passage (Çiçek Pasajı). My favorite stall is the 2nd or 3rd in on the left that has a few bright red bar height tables parked out front. Mussels are 1TL each here and are large. Order a plate of 5 or tell the vendor how many you'd like, squeeze on some fresh lemon and away you go. There were also a number of vendors offering these in the market on the Asian side at .75TL each.
If you're hungry for crispy and slightly greasy borek while walking Istiklal Caddesi, check out Borek Center (delicious spiced beef was our favorite flavor, one portion enough of a snack for 2 at 5TL).