Bit grumpy but still lovely house of mine which was renovated recently is located in old Tbilisi.
House is quite comfy especially for groups of friends, families with their kids and guests. Right next to the house there is a mini market which comes in handy from time to time. But more than I am sure you will love the fact that within 5 minutes of walk you will be in Meidan where there are all kind of things, old remarkable places, Cafe-bars, etc.. Nearby there is also Botanical garden.