How good do you already know Munich? Since a few months is the Pinakothek der Moderne open, fun museum.
Within Munich is the Nymphenburg castle, also has a wonderful exhibit of old carriages and such.
Take the S-Bahn to Schleißheim, another castle plus a branch of the Deutsche Museums - airplanes.
The Deutsche Museum itself is fun also, just a short walk from Isartor.
The only problem of driving to Neuschwanstein on weekends is the traffic (skiing, sightseeing), so bring some time and patience.
There is in Munich the Residence (where the Opera is next doors), they have right now a big exhibit on royal furniture, the building itself is pretty impressive too, not sure how much they show you on normal tours.

Complete list of all castles that belong to the government:
http://www.schloesser.bayern.de/deut...loss/index.htm

What is fun is driving out to the lakes, maybe going for a walk and either drive up or walk up to Andechs, drink some of their famous beer.
In summer its a fun trip to drive to the Chiemsee, take the ferry to Schloss Herrenchiemsee, walk around, see the castle, eat lunch. Lake is now probably frozen.
Also fun is driving to the Bodensee, take the ferry to Insel Mainau, its a beautiful flower island. Again, more a summer option, right now its a white winterisland.

I am in for something, as long as it does not involve Neuschwanstein (I was so bored there, we fled through the emergency exit...)