Mehul, first I am going to publicly defend you against all the criticisms that are about to come your way for renting a car in Brussels...
Having spent A LOT of time in Belgium (particularly in areas ignored by tourists), I would not fault the decision to use a car for day trips from Brussels. The rail system, of course, is better than the US, but not nearly as extensive as Germany, France or Britain, and in many regions, the bus schedules are only published in French and Dutch.
Having said that... I know of two parking garages near the Grote Markt (sorry, Flemish my wife won't let me use the French terms!). One sits to the north, between Wolvengracht and Schildnaapsstraat. The other sits to the south, up the hill from the Grote Markt, near the intersection of Cellebroerstraat and Keizerslaan, several blocks from the Brussel-Centraal station. Neither of these, however, is cheap, and the parking spaces are tightly packed together.