Brussels is not extremely big and it is easy to move using the underground or busses, running until midnight.
The underground has 3 lines, lines 1A and 1B connecting the East to the West of the city, and Line 2 running from the North to the South.
Busses cover the entire metropolitan territory.
The bus ticket costs 1,50 euros if you buy it on the bus. Otherwise, it is possible to buy 10-ticket carnets for 10 euros.
To rent a car, it is possible to address to Rent a car in Bruxelles National Airport, or to Hertz in Charleroi airport.