Trausnitz Castle is the reason to climb the hill above Landshut. It began with the city's foundation in 1204 and later became the seat of the dukes of Lower Bavaria, so it feels less like an isolated fortress than the upper half of the city.
The courtyards, arcades, old ducal rooms, and views over the Isar valley make it worth more than a quick look. If you are visiting during the Landshut Wedding festival, the castle becomes part of the theatre; in quieter years it is the best place to see how much medieval Landshut still survives.