Georgians get along just fine with Russians. It's Putin they despise. Many Russian tourists visit Georgia. Many Georgian adults speak Russian in addition to Georgian.
For interesting architecture, visit Old Rustavi-x. It's a city with beautiful, decaying, patina'd buildings of the Stalinist era. (Unfortunately, you won't find the real Rustavi-x in the LP; instead there's some village the LP identifies as Rustavi-x.)
But the real Old Rustavi is only about 40 minutes away from Tbilisi. You can take a marshrutka from various points in Tbilisi to Old Rustavi-x for only 1 lari and 30 tetri. The marshrutka will drive through New Rustavi-x, then over the Mtkvari River into Old Rustavi-x.
Both New and Old Rustavi-x are quite walkable. You can get a marshrutka back to Tbilisi as late as 10:00 p.m.
Before you get onto a Rustavi-bound marshrutka, ask "rustavi meria"? The meria is the city hall in Old Rustavi-x. It's a giant plaza. This just ensure you are on a marshrutka that goes all the way to the Old part of the city instead of ending in New.
At the plaza are two restaurant/bars with good food: Hollywood's and Giorgi's. Good pizza. Just be sure to say you don't want mayonnaise on the pizza if you decide to order one.
Kutaisi also has interesting architecture in its old town.
Edited by: mzurie