We went in October a few years ago. The trees were changing color and were absolutely gorgeous. We had a car so we stayed in one of the guesthouses in the village of Hohenschwangau; I think it was the Hotel Mueller. We did not have a reservation but had no problems getting a room with breakfast at a very reasonable rate - since it was the shoulder season.

If you really want to splurge, you might consider the Hotel Rubezahl near Fussen. We were able to stay two nights in one of the apartments at a really discounted rate by not making an advance reservation and just asking about availability at the reception desk The website is www.hotelruebezahl.de We had a balcony with a view of the schloss; it was amazing in the moonlight. Our rate included breakfast. They also offer spa services at an additional cost.