In reply to 67hours:
I was in Georgia Oct/Nov/Dec 2011 I probably spent a couple months in total as I visited Armenia in this time as well as. The weather turned unseasonally cold the moment we arrived so we didn't get a lot of stuff done in the mountains. But there is tons of stuff to do and see in Georgia and Georgia is really trying to promote tourism so if you are short of ideas/accommodation/etc. then pop to the local tourist office, they are very helpful.
Here are my top tips
Tbilisi - Not sure on your budget/accommodation preferences but I'd recommend Why Not? hostel (
http://whynothostels.com/tbilisi/index_tb.html ). Misha, was running it, a Polish mountaineer who is passionate about Georgia. His alternative Tbilisi city tour is worth going on. + eat tons of khachapuri (cheesey bread) and drink loads of Georgian wine, go to the baths, go and see the opera or ballet for pennies. (
http://snowleopardsandcossacks.blogspot.com/2011/12/georgia-first-impressio... )
Homestays - out of Tbilisi there are a lot homestays (sometimes these are the only accommodation options) cheap and a great way to stay with locals. People will hang out at bus stations/taxi ranks to offer rooms or the bus driver may have got there first and already got your business!
Churches - there are a lot of them!
Kezbegi is worth a visit and easy to get to from Tbilisi. Easy to organise hikes etc. (
http://snowleopardsandcossacks.blogspot.com/2011/12/kezbegi-mountain-and-ch... )
Gori - Stalin's home town. The Stalin museum is a little scary, no hint of any of his actions being bad, and it has his death mask. I don't think anything was in English only Russian and Georgian. (
http://snowleopardsandcossacks.blogspot.com/2011/12/gori-stalin-and-south-o... )
Cave dwellings - like churches they are everywhere.
Borjomi - Largest forest National Park in Europe (Georgians like to be considered European, some loophole means that they fly the EU flag everywhere). Really nice hiking in the forest. (
http://snowleopardsandcossacks.blogspot.com/2011/12/james-meets-bond-in-bor... )
Kutaisi - Georgia's second city. Stay at Giorgi's homestay in LP. Visit Sataplia State Reserve (not in LP at the time) lots to see including dinosaur footprints where they claim to be one of the few places in the world you can see herbivore and carnivore dinosaur footprints together. (
http://snowleopardsandcossacks.blogspot.com/2011/12/walking-in-footsteps-of... )
Black sea coast - Maybe the most unspoilt part of the Black sea coast. Batumi is a pleasant town (
http://snowleopardsandcossacks.blogspot.com/2012/01/last-trip-in-southern-c... ) and if you are feeling adventurous visiting the break-away state of Abkhazia is interesting (
http://snowleopardsandcossacks.blogspot.com/2011/12/abkhazia-soviet-riviera... ) and has some really beautiful sub-tropical forest down to the shoreline. Here is how to get permission whilst in Georgia
http://snowleopardsandcossacks.blogspot.com/2011/12/how-obtain-visa-for-abk...
Also I'd highly recommend Armenia (
http://snowleopardsandcossacks.blogspot.com/2012/01/armenia-cultural-surpri... ) and Nagorono Kharabakh (
http://snowleopardsandcossacks.blogspot.com/2012/01/nagorno-karabakh-black-... ). There is a long distance trail in Nagorono Kharabakh - ask Misha in Tbilisi for details as he has walked a lot of it.
Sorry that was quite long and may not be entirely relevant. Most of the links are from a blog I wrote. The Southern Causcasus are great. Have a great trip.