Are there any other castles that would be a great day trip from Munich other than Neuschwanstein?
Yes, I can think of at least three not too far away.
In Landshut, Burg Trausnitz. It survived unscathed into modern times, but a fire heavily damaged parts of it in the 1960s. It's a fairly interesting castle, and Landshut is a gorgeous town. I don't think the tour is available in English, though.
Burg zu Burghausen (in Burghausen on the border with Austria) is the longest castle complex in Europe, and the main fortress is also intact and original. The Altstadt is also quite attractive, if not very large.
I didn't think Veste Oberhause in Passau was that interesting... but Passau itself is gorgeous. The castle contains a local history museum. Your enjoyment of it would probably be proportional to your enthusiasm for the historical salt trade.
In my opinion, Germany's best castle is Veste Coburg, in the northern Bavarian town of Coburg, but this is probably a little too far from Munich for a daytrip.
I would agree with Tom about Burghausen, an authentic, never-destroyed castle.
Another one in that category, although maybe a little closer, would be Harburg castle, on the rail line between Donauwörth and Nördlingen. It's a little difficult to get to - a km from town, no public transportation and no lockers at the station, but worth the effort to visit.
While more of a palace than a castle, Herrenchiemsee is about the same vintage as Neuschwanstein. It's an excellent day trip from Munich, especially on a nice day since you have a boat ride to the palace island which has wonderful gardens and fountains. Crazy King Ludwig built it as a model of a mini Versailles. Good exhibit about him there, too.
Maybe this will help and I selected Bayern (Bavaria):
http://www.burgen-und-schloesser.net/bayern/
Take a look at the map link and scroll to the Munich area. You can also check the other Germany States, like Baden-Württemberg.
Thank you everyone. I will take a look at all of those and hopefully get my husband to choose one :)