Hoping to add to the intelligence on this great city. A few places, visited during a week stay in August, 2007.
The best of the Russian ethnic cuisines. Lots of dishes with eggplant, walnuts, pomegranate, fresh spices. Meat dishes include khinkali, dumplings stuffed with spicy meat, and kebabs. Definitely try the khachapuri, varieties of cheese stuffed soft bread.More like Turkish or Persian food than Eastern European.
Two good places: Cafe Tiblisi, Sytninskaya Ul. 10, near the Peter and Paul Fortress and Gorkovskaya metro stop behind the Sytniy food market which also merits a visit. Nice airy interior, off-putting exterior, go inside anyway! I had an excellent lunch dish of green beans, ground walnuts and corriander wrapped in a lavash. The baklava (which is paklava here) was the only disappointment. Not sweet enough for me but otherwise great meal. Not cheap, like $25 for a dinner, but not pricey either. Worth the trip.
Another Georgian place, less expensive is at 3 Kirpichniy, very near the Kazan Cathedral or Hermitage but not too touristy. The name starts with Ne but the lettering on the sign is so ornate I couldn't make out the second word of the name in Cyrillic. Very good khinkali.
An alternative to Russian cuisine is Sukawati which bills itself as Indonesian but more pan Asian. It's at 8 Kazanskaya.
The chain story--Teremok, which serves tasty sweet or savory bliny out of little stands and a few sit down places, is EVERYWHERE and is good when you don't have time for a full meal. Their kvas, the Russian drink (no alcohol, no caffiene) made from fermented rye, is just right on the sweet to sour scale and a terrific thirst quencher in 90 degree summer St. Petersbug.
Leto, a competitor chain, is pretty horrible. (I would like to mention I did not eat there by choice!)
Finally, maybe this is obvious, but you will really do yourself a favor in terms of eating and getting around, particularly the architecturally stunning subway, if you at least learn the Cyrillic alphabet well enough to sound out names. Some places (including most of those above) do have English menus but smaller places do not, and English is not widely spoken outside the more touristed areas. I do not speak Russian beyond simplest phrases but people were HUGELY patient with me and my pronunciation with menus.
It is an absolutely fascinating city! I wish I'd had more time.