I live in Tbilisi, Georgia and find it to be an incredibly do-able country. Beautiful scenery, interesting, outspoken people. I'm happy to provide more recommendations, if you want to provide more specific questions. For a general approach to what it's like here, you might want to check out
http://www.talesmag.com, a website for expats who live overseas.
Depending on how you "do" Georgia, you'll find it very reasonable pricewise. Depending on your travel experience, I would recommend renting a car and driving out into the countryside (Gori for Stalin's museum, David Goreji and Udabno -- unREAL moonscape, Kakheti and the Caucuses mountains, Kazbegi). Lonely Planet doesn't really do much justice, but if you triangular between that and a good road map (from amazon.com, bring with you) you can find a good two weeks of travel. The country is child-friendly, and crime is overrated (unless you walk around with money hanging out of your pockets). I've been here 9 months, and reall like it!
Passport stamp (no visa) upon arrival for Americans, good for 90 day visit. Fairly good English spoken (especially in center).
And go rent "Since Otar Left," a great foreign film shot in Tbilisi.
Enjoy your planning!