A bit wild but super authentic, good for 4-5 days’ trip.
Everyone who’s been to Georgia has stories about the endless hospitality of the locals.
Ski resorts
Bakuriani: 2.5 hours by taxi from Kutaisi
http://ski.ru/az/blogs/post/iz-bakuriani-s-lyubovyu/ (in Russian)
Gudauri: …
Budget
Plane from 100eur, Wizz Air direct (... now).
More info
EU citizens do not need a visa.