Will you have or consider a car? what do you consider 'fun'?

I prefer the less touristy, smaller, but fascinating Schloss Linderhof. The grounds are a pleasant stroll and less crowded than the often packed Neuschwanstein. The grounds including interesting diversions such as the Moorish kiosk and the Venus grotto. I often drive here for an energetic walk around the grounds (so long as there is not snow on the ground; then the outbuidings and fountains are not open) A day trip could include Linderhof, a stop to see the painted houses in Oberammergau, a short visit at the monastery at Ettal, and then a nice meal and small tour of the towns of Garmisch-Partenkirchen. That is one of my favourite day trips.

I also agree with the day trip to Salzburg. Take a short break on the way back at Chiemsee - either just to enjoy a snack by the lake on the Autobahn rest area, or better yet a short drive to Prien if time permits.