Public transport in Tbilisi
Photo Source: city.kvira.ge
Firstly, if you do not have a host who can pick you up from the airport (either at Tbilisi International Airport or the Kutaisi and Batumi Airports), you might need to pay for local transport to the city centers. Tbilisi International Airport offers railway, bus, and private cab options with prices that vary from 0.20 USD to 10 USD. Local transport in the cities cost about $ 0.20 (Bus, metro) and the minibuses (marshutka) cost $0.30. Private cabs are also quite cheap and if you travel with a partner, both of you will pay maximum $2.00 most any destination in the city center.
The train from Tbilisi to Batumi costs $10, buses cost $8.50 and a taxi for four people cost $50. Marshutkas to other places like Kazbegi, Gori, Sighnaghi cost around $2-4 each way. 10 days transportation in Georgia ~ $55. $115 is still in your pocket, which means you have $38 more than the average Georgian pensioner gets each month.
Tip: For a private transport, try some mobile applications, like taxify. They can make getting around a bit easier. Hitchhiking is generally safe. Also take into account that private cab drivers are keen to ask more from tourists (as in most tourist areas) so haggle their prices in advance. This is one difficulty, which can be avoided with mobile apps.