Getting from Kutaisi International Airport to Kutaisi city is easy. As the airport is by main road leading to Kutaisi, even hitchhiking is an option. Leaving that out, here are more comfortable ways to get to Kutaisi.
Transfers vs buses vs taxis
There are three main options for traveling to Kutaisi. Which one is the best for you?
Tip, moving between city and airport should not cost over 30 lari or ~9€.
Most flexible - transfer from your accommodation
To get to Kutaisi from the airport I had my hostel organize transfer. They confirmed in writing it will be 25 lari.
At the end driver asked 30 and I was exhausted from early flight so... paid 30 and left it at that.
Transfers advantage is that it will take you straight where you are going, just as a taxi will. By bus you'll get to city center and have to find your way from there.
Taxis - outside the airport vs Bolt app
You can be sure there are taxis outside the airport waiting and drivers will kindly (read: loudly) offer their services to you. Maybe even asking 50 or 100 lari. In this case a firm "No!" and offering 20 should settle things. They'll either compromise or try to find another traveler.
What if you don't want to negotiate? Use Bolt taxi app. All clicks and no talk. There are many app taxis at the airport too.
My Bolt ride back to the airport from further side of Kutaisi cost 25 lari and took under half an hour.
Georgian bus company Georgian Bus (Wonder how they came up with the name...) is the cheapest way to get to Kutaisi center. At the moment of writing, 25th of May 2020, bus ticket costs just 5 lari - that's about 1,5€.
You can count on getting to Kutaisi center with them but final stop is not mentioned on their website. Maybe this info will be sent to buyers via e-mail, like airport transfer info was sent regarding Georgian domestic flight?
Kutaisi Airport is located by a main highway that leads to Kutaisi, so throwing thumb up by the road could work. I'm not an hitchhiker myself so can't comment on it further. Have you hitchhiked from there? Let me know in the comments!
Preferred transportation - taxi via Bolt app
All in all, maybe after long flight you would like to avoid negotiating with taxi drivers? Then ordering taxi off an app would be most convenient.