One of the most remarkable places nearby Brussels must be Tervuren! Originally it was meant as a resting place between the traveling from Brussels to Leuven, both very important cities in early royal days. Kings and royalties have had their residence here and I would strongly suggest you read about the history on my my VT Tervuren page, although it is still not completed yet. Leopold II, King of Belgium would make this place famous because he used this as an off the beaten path location for the World Fair and held his colonial world fair here to introduce the Congolese colony to the Belgians. Purpose was to build an international institute for Africa but those plans haven't been realised because Leopold II died. However he left us a brilliant Africa Museum and a beautiful park surrounding it, called the Warande.
Website
http://www.tervuren.be