Brussels has an outsized reputation for food, partly earned and partly inherited from France. The local dishes to try are moules-frites (mussels and chips), stoemp (mashed potatoes with vegetables and a sausage on top), carbonnade flamande (beer stew), and waterzooi (a chicken or fish stew in cream). The Saint-Catherine quarter is the traditional seafood area — a cluster of brasseries around what used to be a fish market. Rue des Bouchers near Grand-Place is a tourist trap; avoid the touts on the street and head to the few properly good places on the adjacent Petite Rue des Bouchers.
For something less touristic, Chatelain in Ixelles has Brussels' most interesting restaurant scene, and the Flagey/Saint-Boniface area has a mix of Moroccan, Portuguese, and modern European kitchens. Fries (frites, not French fries — they were Belgian first) are a genuine institution; the fritkots (fries huts) at Place Jourdan, Place Flagey, and Maison Antoine are the classic stops.
Do not leave without eating waffles from Maison Dandoy (the proper Liège waffle, with crunchy sugar), or chocolate from any of the small chocolatiers around Place du Grand Sablon — Pierre Marcolini, Wittamer, Mary, Passion Chocolat.