The centre in one walk
The Grand-Place is 68 by 110 metres of cobbles, enclosed by guildhalls rebuilt after the French bombardment of 1695 and by the town hall, which survived it. Look up at the gold on the facades, then walk out through the Galeries Royales, the glass-roofed arcade from 1847, to the Sablon and the Marolles. The whole route is about a kilometre and takes an afternoon if you let it.
Manneken Pis stands three streets south of the square, 55 centimetres of bronze on a fountain, the original now in the City Museum and a replica on site since 1965. It is smaller than everyone expects. The Sablon has antiques and chocolate; the Marolles has the flea market and a rougher edge; the Mont des Arts gives the postcard view back over the roofs.
Walk down to Sainte-Catherine, where the old fish market became a square of seafood restaurants, then along the canal to Molenbeek. The centre is compact, but the city is not: Brussels is nineteen municipalities, and the European quarter, Avenue Louise and Forest all feel like different towns. Take the metro for those, and keep the centre for walking. The canal end is quieter and has the better view.
Lambic and the bars
Cantillon, in Anderlecht, is the last traditional lambic brewery inside Brussels: founded in 1900, brewing in the same building, with a coolship in the attic and barrels older than most of its customers. The visit is self-guided for most of the week and guided on Saturdays, and ends with three samples. It is a working brewery, not a museum with a bar attached, though it is also the museum of gueuze.
The bars are the other half. Moeder Lambic has two rooms, one near Place Fontainas and one in Saint-Gilles, with forty taps and staff who will steer you towards the sour end. A la Mort Subite keeps its 1928 Art Deco interior and pours its own gueuze, softer and sweeter than the lambic houses. Poechenellekelder, opposite Manneken Pis, has puppets on the walls and a long Trappist list.
Delirium Café claims the largest beer menu in the world, which is both true enough and beside the point: the room is loud and the list is a catalogue. The better evening is a small bar in Saint-Gilles or the Marolles, where the beer is chosen by someone who drinks it. Brussels rewards walking away from the Grand-Place, ten minutes in any direction.
Practical
Brussels-Midi is the Eurostar terminal and the main long-distance station; the centre is a few metro stops away. Gare Centrale sits a few minutes' walk from the Grand-Place, mostly underground. Metro tickets are sold at machines and are valid across trams and buses for a set time, and contactless bank cards work on the newer gates. A single ticket costs more at the driver than at the machine.
The Grand-Place is crowded all year and worst at weekends and in December. Pickpockets work the square and the station; keep bags closed and phones out of back pockets. Restaurant touts on Rue des Bouchers will call you in — the food there is not terrible and not good. Walk two streets to Sainte-Catherine or the Marolles instead, where the menus are shorter and the prices calmer.
Cantillon closes on Wednesday and Sunday and on public holidays; Saturday tours need booking. August empties the city as residents leave, which makes the centre bearable and some restaurants closed. Sunday morning in the European quarter is deserted in a way that is worth seeing once. Cash is less necessary here than in Flanders, but small bars still prefer it.