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Try Lingua House Tbilisi, in the Vake district.  They always test native speaking english speakers for upcoming new teaching jobs, to see if the new person checks out and fits in with the style of the school/experience level.  nice location, good pay for the across the board low scale of georgia.  local number 294 57 07  or mobile number 595 50 29 57.  google them and see for yourself.

or you can try Teach and Learn with Georgia

There's a great blog written by Neal Zupancic. Google it; I'm not a friend or supporter, but an avid reader. He gives very good information about day-to-day life in Georgia.