For the most part, castle were built on the high ground, to command the area, so you will usually have to walk up a hill to see one.
I'm not sure about the walk from Burghausen Hbf to the front of the castle, but there is a bus. I took the bus from the Bahnhof to the Altstadt where I spent the night, then walked up the path to the castle. It wasn't a strenuous climb.
Nürnberg castle is up a hill, but not as far up as some castles.
Harburg, between Donauwörth and Nördlingen is on a hill, but not as long a climb as Neuschwanstein.
Hohensalzburg is high above Salzburg, but there is a funicular from town to the castle.
In Baden-Württemburg, the castles are a bit too far for a day trip. Burg Hollenzollern is on a high hill, but there was a shuttle bus from the base to the castle. The castle at Sigmaringen is on a bluff above the Danube, but the town of the other side is not much lower. But it is a bit of a walk uphill from the Bahnhof to the town.