Very easy to get around Brussels. SNCB.be is the Belgian railroad website; the "Airport City Express" goes to central Brussels (Gare Centrale) and the main train station where long-distance trains leave (Gare du Midi- in a rough part of town).
It's a small city so it's very walkable and the subway and streetcars are great.
Avenue Louise/Louizalaan is the main spot for high-end stores, restaurants, etc.
Go to Bruges, too- about an hour away.
I want to go now! I love Brussels!