Honestly don't go to Neuschwanstein it's nice - but to far for a 3 day trip. It will take you a whole day. When I have friends over from the US we usually only do it, when they stay for at least a week. It's nice - but the tour itself is like 30 Minuntes. It's nice but there is better stuff to do with limited time.

3 days is not much, you will be tired all the time anyways. So just stay in town and maybe do the train to Salzburg.