At first, when Kutaisi International airport was built there were no normal transport options to get at least to Kutaisi, just taxi, which was and still is pretty costly. One way direction from Kutaisi city centre to Kutaisi airport costs about 20GEL. If you are really on budget you might get from Kutaisi airport to Tbilisi, Didube for 10-12 GEL by using Batumi - Tbilisi marshrutka.
But let's not be greedy - There is great alternative, called Georgian Bus, which offers cosy mini-buses both to Tbilisi and Batumi, for 20 and 15 GEL.
Even more, 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 Georgian bus, when flying to Kutaisi.
About Georgian Bus:
Georgian Bus is the first company offering all customers online ticket bookings system and shuttle bus service from Kutaisi International Airport.
Book online at http://www.georgianbus.com/ or meet Georgian bus staff members at Kutaisi airport.