Neuschwanstein day trip from Munich

Do it you self with the train, it will be a whole lot less expensive than taking one of those 3rd party tours, who only babysit you out to the castle. Get a Bayern-Ticket. Book your castle tour ahead of time on the castle website.

I opted to use a guided tour for Neuschwanstein rather than go on my own, and was very pleased with it. This is the one I used - https://www.radiustours.com/tours-in-english/neuschwanstein-castle/ . I often travel solo and it was nice to be with a small group as well as having a guide. I used the same firm for a tour of Dachau.

There is a lot more to see in the Garmish/Fussen area than the fake castle at Neuschwanstein.

Do the Zugspitze, the tallest mountain in Germany. Take the cog train or cable car.
King Ludwig had other castles in Bavaria,
https://www.tripadvisor.com/Attractions-g187293-Activities-c47-t6-Bavaria.html

I often travel solo and it was nice to be with a small group as well
as having a guide.

But whether you go out to Neuschwanstein with a group or on your own, you get the same tour of the palace with the palace's own guides.

All Radius does is babysit you on the train and bus to the town (Hohenschwangau) down the hill from the castle. And they get about $90 to do it! You still have to pay for Neuschwanstein admission either way. Even one person with a Regio-Ticket Allgäu-Schwaben only costs you $35. And if you're already on a Deutschland-Ticket, it's free if you go on your own.

King Ludwig had other castles in Bavaria,

No he didn't. They're all palaces, and non other than Neuschwanstein even resembles a castle. I've been to both Herrenchiemsee and Linderhof. Herrenchiemsee was, in my opinion, a bust. Just a second rate knockoff of the palace at Versailles.

And the main building at Linderhof was a disappointment; just a house, a few rooms for him. But the ground were nice. The Grotto is particularly impressive. But Linderhof is in no way a castle. If you want to see a real castle, go to Harburg or Burghausen.

I have done this twice- once as part of an organised tour, and once as a private group tour when I was travelling with a bigger group. Unfortunately I can't remember the name of either company, but they were both very good. Both times we were driven in a van with several other stops in addition to the castle- across both tours this included local villages to visit Baroque churches, a "little organic cheese farm" for lunch, Oberammergau (very nice Bavarian town), and lunch on a beautiful lake just over the border into Austria. We also really enjoyed the stop to visit Linderhof, Ludwig's other (much smaller) palace, where he actually lived, which also has very nice gardens. I would say have a look at the options for tours and choose based on what the other stops are and what interests you.