The Valkhof Museum sits at the edge of the park bearing the same name and holds the city's main collection of archaeology and art. The Roman gallery is the strongest section: Nijmegen (Roman Noviomagus) was one of the largest Roman settlements north of the Alps, and the excavated finds here — helmets, cavalry masks, everyday objects from a garrison city — are genuinely impressive. The medieval collection covers the Carolingian and later periods, giving context to the ruins just outside.
The art collection is smaller but includes Nijmegen-born painters and some decent 17th-century Dutch work. The building itself, a late 1990s design cantilevered dramatically over the river slope, is worth a look as architecture. The museum café has a terrace with views down to the Waal, which on a warm afternoon is as good a reason to visit as the collection.