On our three-week trip through Georgia we (with wife and three teenagers) of course found time for the beautiful mountains too. We didn't climb any, but observing was already very nice.
From Mestia we took the chairlift up to the top of the ski resort opposite Mestia, to over 2,000 meters, where we were rewarded with beautiful views. We kept turning to Ushba, which enchanted us with its sheer walls.
https://www.youtube.com/watch?v=4LSF6KZLZWA