I was "lucky" to be in Tbilisi on Graduation night. There are a lot of people and loud music in every cafe/restaurant. Despite this, we were provided with a beautiful detached house in this institution, where it was quiet and we were alone.
Khachapuri in Adjarian is very tasty, herbal tea too.
A Russian-speaking girl served us (unfortunately we didn't think to ask her name), quickly suggested the menu, quickly brought food.