Tbilisi has a long tradition of café culture. Cafe Theatre reinvents the art of the Tbilisi café by combining art, music and theatre with excellent food and drinks. Typical evenings include finger puppet performances and jazz. I like it because it is quite central, right in the thick of all the night life in the Old Town. They do still have smoking indoors, which might be a bit of a turn-off for a lot of people. Once I get used to it, I quite like the haze it creates. It reminds me of an old-time jazz cafe.
Cafe Theatre is right next to the sulphur baths. Stop by before a tea to keep you energized for the baths, or stop by in the evening and catch a live performance ranging from traditional Georgian to jazz tunes. The espresso-based beverages are quite good and the food is of good quality.