Brussels is extremely well placed for day trips into Belgium and beyond. Three of the country's great cities are within an hour by train: Bruges, with its medieval canal network and chocolate shops; Ghent, which has much of Bruges' beauty with fewer tourists; and Antwerp, with its diamond trade, Rubens museums, and excellent nightlife.
Waterloo (20 km south) is where Napoleon's army was finally broken in June 1815. The battlefield is well preserved, and the Lion's Mound — a conical earthwork raised on the spot where the Prince of Orange was wounded — gives a panoramic view across the fields where the fighting was heaviest. A small museum covers the campaign in detail.
Tervuren (15 km east) holds the Africa Museum, which covers Belgium's deeply uncomfortable colonial history in the Congo — a serious and thoughtful institution that makes no attempt to gloss over what happened.
Ghent is particularly recommended if you only have one day outside Brussels — the city centre is compact, the Ghent Altarpiece in the Cathedral of St Bavo is one of the great artworks of European history, and the Graaslei and Korenlei quays rival anything in Bruges for beauty.