Hi,
The answer would be too lengthy to type in here. If you are still around in Belarus or plan to visit it this year ( summer is the best time, of course), drop m a line. I've got good friends, dedicated to their city and with a good profound knowledge of both old traditions and modern customs to advice you on sightseeing, leisure trips, nature walks, etc etc,
In two words, Minsk does not offer TOO many places/things/ to see/visit, but some are worthy as they are quite unique among ex-USSR members and offer their own style, different from the EU's. But be prepared for financial expenses. Minsk isn't cheap anymore, anywhere.