The NY Times just did a 36 Hours in Moscow article that has some good recommendations:

http://www.nytimes.com/2010/10/03/travel/03hours.html

I really like Kvartira 44 and Khachapuri, and neither will break the bank. Strelka has been one of the places to see and be seen over the summer, but the outside dining has gone bye bye.

If you want a little Soviet kitch right on Red Square, try Stolovaya 57 in GUM - third floor, third row (I believe):

http://www.inyourpocket.com/russia/M...vaya-57_40336v

It is a true cafeteria as the Russian name suggests, you gotta get a tray and bus your own table, but they have all the Russian favorites and it will easily be the cheapest meal not served on the street within a kilometer of Lenin's tomb.