Kala is the innermost historic core of Tbilisi, the area between Freedom Square to the north and Sioni Cathedral to the south. This is the densest part of the old town: the streets are narrow enough to touch both walls with your arms outstretched in places, the buildings overhang above, and the occasional glimpse of a courtyard reveals private worlds of washing lines and cats and fragrant cooking.
The main sights — Sioni Cathedral, Anchiskhati Basilica, the Puppet Theatre, the Ashkenazi Synagogue — are all within Kala or on its edge. But the best way to experience the area is to stop looking for specific things and simply walk: turn down whichever lane looks most interesting, accept the occasional dead end, and allow the place to reveal itself gradually.