Bad Aibling to Neuschwanstein will be a minimum of 2 hours each way, plus there is always a queue to get into the place. I guess it's impressive to see once, but let me give you another suggestion...Ludwig's other grand project was Herrenchiemsee, a Versailles reproduction on an island in the Chiemsee, which is much closer to you (say 30 minutes). You take a ferry over and walk to the castle. It's quite impressive and you can see where building stopped.

Hiking in the Berchtesgadener Land is ubiquitous.