The cost of living in Georgia. Tbilisi Public Transport
If you are planning to use public transport you should buy the card “Metro money”.
“Metro money” card is a universal mean for payment in municipal transport. The cost of the card is 2 Lari.
Purchasing “Metro money” card is possible to any payment office of metro stations and Rike-Narikala wire rope. The card is not personal, so you don't need ID to take the card.
You can put money on your “Metro money” card in any metro station, both stations of Rike-Narikala wire rope, both stations of a funicular up to Mtatsminda and express payment machines of “Bank of Georgia”.
Tbilisi public transport is Underground (Metro), Bus, Mini-Bus (Marshrutka) and Taxi.
You can plan your trip on Tbilisi Transport Company (Tbilisi Bus And Metro) web-site. Also, the Map of Tbilisi transport system may be useful.
City Bus
The Buses run at fixed times from 7 am till 12 pm. Early in the morning and in the evening they run infrequently. They only stop at specified bus stops.
You can buy a ticket at the ticket machine in the bus for 50 Tetri. The ticket machine doesn't give change, so the fare should be paid exactly or you can use the card “Metro money”.
Metro
The cost for entrance is 50 Tetri. The entrance is only with the card "Metro money".
Each passenger who uses the "Metro money" card while travelling by the public transport (only Bus and Metro) pays 50 Tetri for the first time travel and for the next hour and a half he travels by Buses and Metro for free.

Mini-Bus (Marshrutka)
If you'd like to travel by minibuses, known as Marshrutkas, you can catch it basically at any spot you wish (except: Chavchavadze Ave., Melikishvili St., Rustaveli Ave. and Freedom Sq.) as the minibuses have no fixed stops.
The passenger may ask the driver to drop him/her off at any place he/she desires. Mini-buses usually cost 80 Tetri. They run from 7 am to 12 pm.
The passenger who uses the "Metro money" card pay for the first time travels 0.80 Tetri and for next travels during the day, he pays 0.65 Tetri.
Ropeway and Funicular
Tariff for travelling by ropeway of Rike-Narikala and a funicular up to Mtatsminda Park Cost of travelling in one direction is 1 Lari.
Travelling is possible only under usage of the "Metro money" card.
Taxi
Taxis are one of the quickest ways of getting to a destination. They can be found almost anywhere. Fares are very affordable, and should never cost more than a few Lari. Always verify the cost of the trip before you get in the car.
The price in center regions of Tbilisi is from 3 to 5 Lari. Other destinations are from 5 to 10 Lari. Taxis are everywhere on the main streets, so don't be shy of asking for a good price.
Also, you can call to Taxi service, the tariffs are always lower.
Source Tbilisi Guide
Source Tbilisi Transport Company (Tbilisi Bus And Metro)