First to say, it's as local as it may ever get. It may not be fancy or pretty, but if you want to see the truth - here it is, right behind the big glass windows. You may either hate it or love it, but it's the soul of the city - and you can't stay ignorant to the bar on the first floor.
Old soviet-styled department store with amazing interior and the motley crowd of visitors: dirty hobos, artists, crazy people, local celebrities, students, professors - everybody gets together. Other perks: the cheapest and tastiest desserts in town (and cheapest alcohol too). Head here if you're broke (if it's even possible in Belarus).
I admit it, you may not like it if you're very squeamish or love the fancy rich life. But it's the local life of an average person here, so be fair.