Good areas for tourists that are safe are the area around Central, the centre-ville around Grand' Place and the Ste.-Catherine area, the Sablons area, as well as the Louise / Stéphanie district. To that I would add the European Quarter, where you can find real weekend bargains because the Eurocrats have gone home and are not occupying those hotels.
Areas that are not so good are around Bruxelles-Midi station, Bruxelles-Nord station, and the northern part of the city (near Rogier / Botanique metro, St.-Josse and parts of Schaerbeek, although other parts are very good). There is still plenty of scope in those safe areas to find good accommodation, dozens of good hotels in fact.
Lavandula