What should a tourist do in and around Brussels?

To steal a line from Titus, Dear Lazyweb:

I am going to Brussels, Belgium for AOSD. Because of flight costs I will be arriving the Friday before the conference. But since I have never been to Brussels, I booked my flight home the Monday following, giving me an extra weekend after the conference to do more tourist stuff since I know the jet lag is going to kill a day or so.

But I don't know what to do while I am there. =) I am assuming I can do some stuff at night during the conference, but obviously there is more to do during the day. If anyone has specific pointers as to interesting things within Brussels that would be great to know. Or if there is some place nearby where a weekend visit is worth it that would be great to know as well (since I am flying out of Brussels I don't want to get too far away and burn a lot of time on travel).

And one more thing: if anyone knows a good book on Belgian history I would love to know that as well. I read Winston Churchill's 'A History of the English-Speaking Peoples' when I traveled to England and Scotland and found I loved knowing the history of a place while I was there.