Brussels has quite a compact centre and it can be easy navigated around on foot. Many of the old streets are pedestrian only or their access to cars is limited. There are four Metro Lines and an extensive Bus network running until around after midnight, after which there are night buses (Noctis Lines). All public transport is run by STIB and the best way to go about if you’re planning to use the transport system is to use a MOBIB card, which can be pre-charged with number of trips or special 24 or 48 hours passes.
MOBIB cards can be purchased at kiosks (in main station) and can be recharged at the same kiosks or at over 400 machines around stations, online and even in some libraries & grocery stores. MOBIB can also be used on train journeys within city limits. Single tickets are also available (JUMP tickets) but remember that they are cheaper if bought in advance from the kiosks or the machine, rather than on board.