Bakuriani, beautiful mountain resort near Borjomi is situated at an altitude of 1700 meters above sea-level. You can enjoy it's healthy fresh air in any season.
There are several skiing-routes with different difficulty levels - Kokhta Gora (meaning "beautiful mountain"), Kokhta 2-Tatra, "25", Didveli etc. Skiing season lasts almost from November to March. Here you can enjoy snowmobiles and quadrocycles, skates in the park as well.
You can find comfortable private houses for rent and guesthouses, where prices are quite accessible.
I'm putting several links of Bakuriani hotels as well:
Kokhta ski lift
View from Kokhta
Skiers on Didveli
Didveli cable car
Didveli 2nd ski lift
Skier on Kokhta route
Me and my sister on Didveli :)
Tourists on Kokhta