If you're planning on visiting Brussels for the first time, one of the best ways to see the place is by following the route of the number 81 tram. It leaves from the Montgomery stop, and starts its journey off through the more fashionable inner suburbs (a good way to see some of the Art Nouveau architecture, then on towards the Porte de Louvain where some of the more fashionable shops can be found. From here it goes to the Gare du Midi, where you might want to join it if you've just arrived by Eurostar. Next, it moves in through the historic town centre, where it travels underground (so you'll probably want to walk this part).
After having been to the Grand Place and done touristy such things, rejoin the tram at the Bourse. It now takes a meandering route out through the northern suburbs to Heysel, where it terminates. Here you'll find Kineopolis, a very nice and very large cinema. You could also have a look at the semi-famous Atomium while you're here
This tram line would make a very good pub crawl (akin to the circle line pub crawl) for those who have the stamina.

Alternatively, if you'd rather head out of town, take the number 44 tram out to Tervuren. The scenery along the way is quite pretty, and you may want to stop at one of the parks or the tram museum along the way. In Tervuren itself is the African museum, which is fairly magnificient, and there are more parks and lakes.

Among the reasons for visitng Brussels are drinking Belgian beer, eating Brussels waffles and the aquisition of Chokotoffs.