Use Deutsche Bahn and Google maps to build your own itinerary: https://www.bahn.com/en/view/index.shtml
https://www.google.de/maps/@48.9174128,11.4079934,7z
And check out bus services:
https://www.rvo-bus.de/oberbayernbus/view/index.shtml
If you can't find english translations or need help on identifying the proper town place names for your journey on the website use Googlemap and Google translate.
It is about 1:45 to Salzburg which can make for along day - but great castle, food, Austrian ambience (they specialize in Mozart of course).
Berchtesgaden is a breathtaking place - reachable by train to Salzburg and then a bus (2.5 hrs) , but it would be a very long day.
Or, if you want other Alps there is Garmisch-Partenkirchen an hour and a half south of Munich. Lovely town, and the Zugspitze cog-railway up to the top of the tallest peak in Germany is right beside the DB station. A great hike there is up the Partnach Gorge just south of town going into the mountains.
Andechs Cloister and brewery are about an hour southwest of Munich and are reachable by train and bus.
Of course there is a Bavarian Administration for castles and palaces for details on the many sights:
https://www.schloesser.bayern.de/englisch/palace/index.htm
Neuschwannstein/Hohenschwanngau is reached directly by train through Fussen, and the trip takes about 2.5 hours each way. (Or rent a car for the day). Admission times are allocated ahead of time so try to match travel/admission. Or you can join one of many tours to Neuschwanstein that go out daily from Munich (and they try to get all of the mid-day timed admission tickets).
Linderhof is not really too close to Fussen though. I have gotten there by bus from Garmisch-Partenkirchen. It is lovely and Ludwig actually got to live there, unlike N which was a mostly unfulfilled fantasyland (to me).
http://www.schlosslinderhof.de/englisch/tourist/index.htm
The guides mention everything... It just depends how much you can cram in.
It may seem odd when touring around "Munich," but Nuremberg with its many sights is only about an hour north of Munich by train, and it has wonderful Museums, the Nazi Documentation Center at the old Nazi Party Rally grounds a short tram ride SE of the Bahnhof, and of course a rebuilt castle. Also the Nuremberg Trial courtroom and museum which is a short S-bahn ride west of the Bahnhof. The actual trial courtroom is still used as a courtroom daily, but is open to tourists on weekends.
https://museums.nuernberg.de/memorium-nuremberg-trials/
I assure you will have a great time.
