All the city center you can get around on foot. I recommend to visit Narikala Castle, Statue of King Vakhtang Gorgasali, walk through the streets of the old town, to look into the bath.
The cost of private rooms in a bath 13,6 USD = 40 GEL per hour. If you're lucky, you can find public baths, a price tag in about 1 USD = 3 GEL
Tourist excursions are offered on every corner. Prices for day tours from 34 USD = 100 GEL
There is a sightseeing tour by bus. Prices from 11,9 USD = 35 GEL per 24 hours. Tickets can be bought on the bus when boarding.
Read my review of useful websites to buy tickets for sightseeing tours and attractions
Souvenir shop in the old city center. Negotiable. Also in the gallery exhibited paintings and sculptures by local artists. Price from several hundred to several thousand dollars.
Currency Exchange presents no difficulty. The course is always good, small fork, everything is safe, do not take commissions.