I've been to Brussels, and the obvious things to see in the city include the Grand Place (an impressive old town square), Saint Michael's, Manneken Pis (touristy), and an interesting restaurant/bar row near the old town. These are all within walking distance. I'm sure others can recommend the can't-miss museums, however, we did not go to any of them.

I'm not sure how far away Amsterdam is, but an obvious day-trip on the train is Bruges (aka Brugge). I believe it's approximately one hour away by train.