Stay in Brussels as your home base. It is the largest city, has the most activity and is well-located for day trips throughout the country. Brussels is a walk-able city, and in fact a large part of the downtown area is a pedestrian zone. Shops, restaurants and cafes line the stone streets which after work or on a weekend are filled with locals and visitors. All of the pedestrian walkways meet at the Grand Market, a large pedestrian square surrounded by eateries and exquisite cathedrals which have now been transformed into museums. At night, the square is beautifully becomes quite lively, the local hang out for the young and young at heart. Scattered throughout this shopping district (and other parts of the city) are museums for virtually any interest you might have - various types of art, history and music to name a few.
The business section of Brussels is divided into two distinct sectors. Adjacent to the shopping district is the corporate "downtown" segment. The unique statues, fountains and modern architecture certainly make it worth a walk down to this section as it provides quite a contrast to the cobblestone streets of the pedestrian area. The second part of the business district is centered around the headquarters of the European Union, located on the other side of the city. This complex is currently undergoing expansion and will soon be home to several other notable "attractions" including the Natural History Museum. This very modern building (with surprisingly low security outside) sits on the edge of a tranquil park, complete with walking trails and a lake. I arrived too late to enter the actual EU building, but if I were visiting again it would definitely be on my "to do" list.