Can you go to Neuschwanstein Castle

Its a free day, so yes, you can go to Neuschwanstein if you want. You can take a train to Fuessen, then a bus to Neuschwanstein, You need a timed reservation to tour the castle. Return to Munich the same way you came.

I understand this question because the first time I was in this area I felt that this must really be a "must see" for me. I discovered that I spent a great deal of time and effort just to have a major disappointment. The view of the outside of the castle is interesting, but the inside is a quick 15 minutes sprint through some "not that interesting rooms" to the gift shop.

If you really feel you absolutely have to go see this, I understand. However, I can give you a much more interesting and authentic alternative that is right in Munich. The Nymphenburg Palace Complex is a short tram ride away from the Munich Hauptbahnhof (10 minutes). The Palaces and the grounds are very interesting to explore. I found these a far more satisfying experience and so convenient to anyone in Munich.
https://www.schloss-nymphenburg.de/englisch/palace/

Your hotel may also be able to arrange one of the tour bus companies that will take you there and back.

We did a Grayline bus tour from Munich to Neuschwanstein many years ago. It was a convenient way to go albeit a big bus tour.

I’ve been twice and, It’s not IMO worth a daytrip, but that’s me.

In about 35 years, I've been in Füssen 6 times - 4 times for castle visits (either Neuschwanstein or Hohenschwangau), twice just passing through and spending a little time going to/from Pfronten. I would never consider Neuschwanstein a waste of time. It's a beautiful edifice and an interesting window into the life of an eccentric king. As long as you read a little about it before you go and don't expect to see a real, medieval castle, it's worthwhile. Do the trip on your own by train and bus. I don't think it's worth the high price of a canned, third party tour.

However, with only one day in Munich, I don't think I'd venture out of the town. There is so much to see in Munich - the area around Marienplatz and Frauenkirche, Deutsches Museum, Nymphenburg, Dachau. If you are in Munich, don't miss the opportunity to see Munich.

Fall in love with Munich and come back later to see more of it and also visit the area south of the city - Mittenwald, Garmisch-Partenkirchen, Linderhof, Oberammergau, Füssen and the castles. I love the Oberallgäu - Oberstdorf, upper Illertal, Kleinwalsertal is beautiful and not often visited by Americans.