Zug Castle is a compact medieval tower-house on the lakeside, now housing the Museum of Prehistory and History of Zug. The collection covers the region from the Ice Age through to the early modern period, with strong material on the Roman-era settlement around Lake Zug and the medieval town that preceded today's city. The museum's displays are solid without being spectacular — worth an hour if you're interested in local history.
The castle exterior, with its distinctive round tower and whitewashed walls, is more photogenic than the interior. It sits at the lake's edge on the southern side of the old town, with a small waterfront garden that offers good views across to the mountains.