Posted this below in the Russia section. Dont know where I got it, but I went to one of the places listed below called The Mill. Pretty decent.




There are (at least) two good Georgian restaurants within a reasonable walk of the National. The closest is Genatsvalle, which is located on Ostozhenka in the vicinity of the Christ the Saviour church. The hotel will know it. The other is also on Ostozhenka, but a bit further away. It is called Tiflis. I actually like Tiflis a bit better, but both are good. One item - any really good Georgian restaurant is likely to exceed your $50-$60 budget.
My favorite Russian restaurant is called Glavpivtorg, and is located near the Lubyanka Metro station. Actually, it may be my favorite Moscow restaurant, period - Russian or otherwise. Very tasty dishes - try the pressed chicken (big enough for two) and Borsch. Both are quite good, as well as their home-brewed beers. It is walkable from the National, in maybe 15 minutes. You can easily get your fill there within your budget.
Another good, reasonably-priced Russian place that is more than a little walk (located on the Garden Ring, near Krasnye Vorota Metro) is Na Melnitse (The Mill).
The best Uzbek restaurant in town is called simply, "Uzbekistan." It is well worth a visit, just to taste the plov (saffron rice and lamb) and their baklava (Russians call it Paklava). It might be over your budget by a little, but not too much. It's worth it though. Mmmm.
For a budget Russian meal, eat at one of the many Moo Moo locations around town (spelled My My in Russian). Serving lines (you can simply point at what you want, if you don't speak Russian) and hearty, cheap Russian food make this place worth a stop. There is one on Tverskaya Street, just up from the National, maybe 300 meters, and another on Arbat street.
Also near the National is Kamergersky Pereulok, which is a side street off Tverskaya that has been closed to traffic. This pedestrian street is lined with restaurants of all sorts, but very few ethnic sorts of the type you have mentioned. There are about 3 decent Italian places, at least one Chinese place and a high-end Swiss/European place, called Cafe des Artistes, which is very good, but well beyone your stated budget. Akademia, however, is on this street, and is quite a good, reasonably-priced Italian restaurant.
Another popular ethnic chain around town is Shesh Besh (Azerbaijani). There is one located on Arbat street, which is walkable from the National, but there may be one even closer that I'm just not aware of.
I haven't eaten at any specifically Ukranian places, and most of the people I have asked can't explain the difference between Russian and Ukranian food, but there is a Ukranian chain called Taras Bulba, which has locations around town. One such location is on Pyatnitskaya Street, south of the Kremlin and across the river, which would be a bit of a walk from the National, but if you really have to have your Ukranian...