Although Brussels has quite a few (small) parks, on a sunny weekend day most can get very crowded. The green campus of the Vrije Universiteit Brussel (Dutch speaking counterpart of ULB, Free -as in independent from state and church- University of Brussels) in Etterbeek (which is actually officially on the territory of Elsene).
During weekends and university holidays it can be quite empty and the bars on campus (KultuurKaffee, 't Complex, Opinio) are closed. But there is plenty of greenery to enjoy some quiet time, throw a Frisbee or whatever.
There's also a sport complex with swimming pool, sporting facilities, running track, fitness and all that on campus and it's open to non-students.
KultuurKaffee (free spelling of culture café) is the best place to enjoy a good concert or party. Thursday evening has free concerts ranging from rock to world music. Every first Wednesday of the month there's a free jazz concerts and in the weekends there are often parties going from minimal house to reggae.