My place is a five minutes walk away from metro (subway) station Varketili. From there it is a 10 minutes ride to the city centre. I'll live there myself, occasionally, so the apartment is fully equipped, and probably you won't mind my daughter's toys in some corner. It can be somewhat noisy due to regular (Georgian ;) street trafic, but most guests do not mind, and others simply use earplugs at night. You'll reach the place from the airport by car conveniently without crossing the city centre.
5 minutes walk to subway station Varketili