Brugge is so easy to get to by train, I would just book a tickt at Central Station when you arrive in Brussels. The old city is right at the Brugge station. It is a walking city so you don't really need a special tour. There are lots of wonderful old churches in Brugge and it is a very charming town to spend the day walking around through.
A day trip to Antwerp would be good to. There they have a good zoo, a diamond museum and one of my favorite museums in Brussels, the Peter Paul Rubens home. It is the actual home where he lived and painted and is one of the few existing homes of a famous artist.
In Brussels lived Victor Horta, who is the leading Art Noveau architect of his time. His home is also a museum.
It is located in the center of Ixelles (which is part of Brussels) Musée Horta, rue Américaine/Amerikaanse straat n° 25 . If you do like this kind of arcitecture, he also designed the building (which has been carefully restored) that now houses the comic book museum in the center of Brussels.
You might consider a day trip to the center of Ghent, a midevil city center which houses an old castle you can tour. It is also easy to get to by train.