You know most Georgians speak English, and most of the signs are in Georgian and English. You can do just fine in Tbilisi with English only. I did. Even a last minute taxi I grabbed to the hotel one day was amazingly efficient, as the man sat there and thought for a moment about what I had said, and then figured out what I was asking.
That said I am going to be learning Georgian.
"That said I am going to be learning Georgian."
You'll have to at least learn the Georgian for Kyrie eleison.
Some good Georgian stuff at http://www.geocities.com/Athens/Thebes/1865/