Castles near Munich - not Neuschwanstein Castle

Two I can think of are Burg Trausnitz in Landshut and Burg zu Burghausen in the town of the same name.

Burg Trausnitz managed to survive intact into the 1960s when a fire severely damaged the interior. The floor plan was rebuilt, but only some of the original decor remains
Unfortunately, Ludwig II's lavishly decorated apartments perished completely. Also, tours are only available in German, but they give you an English manual if you can't understand German. Despit's all this, it's still with a look. And Landshut itself is beautiful.

Burg zu Burghausen claims to be the world's longest castle, but the validity of that claims depends on your exact definition of the word "castle". The main fortification, though, retains most of it's original structure and interiors. It hasn't served as a residence for several centuries, so don't expect particularly opulent decorations. The castle overlooks a scenic Altstadt, on the border with Austria.

Personally, I think Bavaria's (and Germany's) best castle is Veste Coburg, but this is too far away from Munich for a daytrip.

Well, for me, the best of the Ludwig castles is Schloss Linderhof, just 15 minutes from Oberammergau. Without question the best interior of any of his castles and arguably in all of Germany. You can take the train from Munich to Oberammergau in about an hour and forty minutes and, once there, either take a taxi or the public bus that runs to the castle. You should be able to research all the connections using bahn.com. And, of course, you'll have the added treat of Oberammergau itself.

Have a great time!

I would second Tom's suggestion of Burghausen, and would add Harburg castle near Nördlingen, on the Romantic Road. It's only about 1 hr 40 min from Munich Hbf to Harburg Bhf via Donauwörth. There doesn't seem to be any public transportation in the town. From the bahnhof it's a flat 1 km walk to town, from which it's a short steep walk up to the castle.

As for Linderhof, if you don't appreciate Neuschwanstein, I wouldn't go to Linderhof. It's a very small Italian-esque Villa, nothing like a castle.

"The less travel time the better (no more than 2 hours by train - preferably less..."

As you can see from the above suggestions, Munich isn't ripe with medieval castles, and you'll be making some fairly long train trips.

Pappenheim's castle is reasonably good (ruined) medieval castle to visit if you're in this area. It's 1.75 hours from Munich on the direct RB train (closer than Burghausen anyway, which is also good.) It's a place few foreign visitors go but a completely enchanting area to be in. Pappenheim is picture-perfect, and the Altmuehltal Valley is very pretty. See Eichstaett too. Weissenburg, also near Pappenheim, is an attractive walled town.

Since your trip includes time on the Rhine already, I think overall you'd be better off seeing the medieval castles there, where there are several good choices nearby, including Burg Rheinfels, Marksburg, and Burg Eltz. With a proper overnight location you could see two of these in a single day if you wanted to. Another castle (rebuilt, not original medieval construction) is Reichsburg in Cochem, which I mention because it's so close to Burg Eltz, and because it offers a falconry show most days of the week, and because Cochem itself is so utterly charming.

Many thanks for the excellent suggestions everyone! I know my parameters are tight (and the itinerary is hard set now) so I really appreciate you thoughtful replies.

My first reply would be Herrenchiemsee. 1 hour travel time to Prien, then a small train to the pier, then a ferry, then a horse cart to the castle. The travel routine may seem long but it is quite pleasant; the earlier you leave, the better. - The castle is not a medieval one, it was built by Ludwig II in his usual fake Versailles style.

For a full size medieval castle, consider the fortress at Salzburg. For a Renaissance castle, Ambras at Innsbruck. I have no experience of the fortress at Kufstein.