Sites around the city, Brno
Spend time in the old, walled part of the city. There's so much to look at even if you don't go inside anywhere. But do go inside -- the old city hall, the churches, the galleries, the clubs and restaurants. Be sure to go up to the top of the old city hall - the view is fantastic. Also, you should try to get a look at the Tugendhat villa, designed by Mies van der Rohe. Sample as many different beers and wines as you can -- Moravia is the wine region, so if you can get invited to somebody's wine cellar in the country, by all means do it! You may have a hangover for several days like I did, but it will seem worth it at the time, anyway.
Fondest memory: I went to Brno instead of Prague because Prague was crawling with Americans at the time (1993), and I wanted to be with Czechs, not Americans. I ended up having a really great time in Brno, for the most part. Living there for 8 months, having a job and an apartment and living on my Czech salary as much as possible made the experience quite different from that of the more transient tourist. 30Kc for a movie started to seem really expensive! even though it is just over $1. And beer more that 15Kc? Outrageous! But we lived as large as possible, and had some great times, probably more than I can remember. On the weekends, we often went on day trips to many of the fun and interesting places that can be found within a short train ride of Brno: Mikulov, Telc, Znojmo, Kromeriz (these names all need to have accents on them to be correctly spelled, but the computer doesn't do that), the Karst region, Hrad Pernstein, and many others whose names escape me at the moment. There is also an excellent network of well-blazed trails, which we made use of on our wanderings. The trails feature frequent signage indicating the kilometers to the next hostinec (place to get a beer).