At first, when Kutaisi International airport was built (around 2012/2013) there were few transport options to choose from to get at least to the city center of Kutaisi, as it turns out, the city is actually located about some 17km from the airport. Back in the days, there were just taxi services, which was and still is pretty costly (as long as you are not using BOLT)
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One way direction from Kutaisi city center to the Kutaisi airport with street taxi cost about 20GEL (price as of 2015). If you are really on a budget you might get from Kutaisi airport to Tbilisi (Didube station) for 10-12 GEL by using Batumi - Tbilisi marshrutka, you can try to catch one, just after leaving the airport building and heading to the highway, which is some 200 meters from the terminal building.
But let's not be greedy - There is a great alternative, called Georgian Bus, which offers cozy mini-buses both to Tbilisi and Batumi, for 20 and 15 GEL (prices as of 2014).
Even more, the Georgian Bus will get you both from Batumi and Tbilisi to Kutaisi airport as well.
Don't get scammed with some Taxi offers for 100, 200, or 300 GEL or even USD. Try the Georgian bus, when flying to Kutaisi.
About Georgian Bus:
Georgian Bus is the first company offering all customers an online ticket bookings system and shuttle bus service from Kutaisi International Airport.
Book online at Georgian Bus or meet Georgian bus staff members at Kutaisi airport.