You can exchange money at banks and exchange offices, "exchangers". Banks operate from 9 am to 6 pm, Monday through Friday while exchange offices operate on a flexible schedule, often around the clock. There are, of course, black market money-changers, but as in all countries exchanging currency in black market is not advised in order not to become a victim of fraud.
There are many ATMs
throughout Tbilisi, in addition near the banks, shopping centers
and post offices. Payment by "credit card" can be done in
hotels, large restaurants and shops, but not everywhere, so you
should always carry cash. In Georgia the network of Western
Union is developed so you can easily get money through Western
Union in case of contingency spending.