Don't get misguided by the word "bar", as this is actually a regular restaurant of the so-called "Caucasian" cuisine, standing for the Georgian & Armenian in this case. The place is easy to find not so far from the Russian musem.
Meals and wine are of good quality, though I expected a variety of vegetables or at least some sauce going with meat which I had ordered. So to avoid unpleasant surpirses ask exactly what is inside!
As there were just a few people/restaurant visitors on a Friday evening, I figured out "Kavkaz bar" was not the best "Caucasian" in the downtown, still with a fancy interior design and good service.
The price range is medium, I 'd say (ca. 20 euro in total per person including wine), the menue card is fun to study!