If you want to go to Davit Goreja, and I highly recommend that you do, this is the place to be at 10.00am on any given morning. The tour company charges 30 Lari for the full day trip, The square is a great place to relax on a few park benches and do some serious people watching as it adjoins Liberty square.

Pushkin Square is near Freedom Square. You need not go there intentionally, but when you are exhausted by walking from the old city to Rustaveli Avenue, you can have a rest there in the company of the great Russian writer. There is shadow due to the high trees and it is a bit cooler than in the surroundings because of a fountain in the square. Unfortunately the air is not very clean because traffic is heavy. Maybe you can get to know the local population there and talk to some Georgian sitting on one of the benches.