Burghausen Castle is the town's great spectacle, a long fortified spine running above the Salzach river and the old town. Rather than a single palace, it is a sequence of courtyards, gates, towers, chapels and former workshops, so a visit feels like walking through a small walled settlement. The main castle at the southern end holds the strongest views over the river bend and Austria.
The complex is free to wander, with paid entry for the museums and some interiors. Start at one end and walk the whole ridge if you can; the scale only really registers after the third or fourth courtyard. Late afternoon is especially good, when the walls warm in the sun and the old town below begins to glow.