The Armenian quarter in Tbilisi. There are many grocery stores, a small market, and cafes... Very close to the old town, which is located much lower, please note when returning from a walk that it is uphill :)
Metro station across the river from the tourist center of Tbilisi.
The area is old, but there are a lot of guest houses in it with prices noticeably lower than across the bridge - in the Old Town proper. There are several cafes in the area, also cheaper than in the Old Town.
There are several exchangers right at the exit from the metro.
The station is in the process of renovation, a small new park with a fountain just behind the station has recently opened.