Neuschwanstein Castle

Last fall we rented a car at the Munich airport and made the approximately 2 hour drive to Fussen. It was a wonderful drive and beautiful city to visit. We ended up spending 2 nights there and got up early on the first morning to make a quick (10-15 minute) drive to Neuschwanstein. We did purchase online tickets ahead of time for the castle which we were grateful for when seeing the long line for same day purchase. As we were leaving the area, it looked as if the tickets were sold out for the day. We really lucked out because the weather was perfect.
There is definitely a day tour to the castle, but we decided to make the trip at our leisure. Before returning our car at the airport, we visited Dachau which was incredibly moving.
Safe travels

Each of these can be done using the Bayern Ticket as a day trip. For 2 people, the cost is 31 EUR and covers all trains, U-Bahns, trams, buses in Bavaria for a day. Mon to Fri you must begin travel after 9 am. Weekends and public holidays you can travel any time.

Going to Neuschwanstein on a week day leave from Hauptbahnhof at 9:52 and get to Fuessen at 11:55, then the bus at 12:05 to get by the castle at 12:13. You will need to get a timed reservation for the castle and you need to check in at least an hour before your reserved time. That way, you can pay for the ticket, and it takes about 15 minutes to walk up the hill to the castle entrance and wait until your reservation time is displayed. So for this, I recommend a reservation time of not before 13:30.
https://www.hohenschwangau.de/1390.0.html

Buses back to Fuessen are pretty frequent, but there might be gaps in the schedule of up to 45 minutes. Fuessen has a nice Christmas market, so you might want to spend some time there. You can take any train back to Munich that evening. Train at 18:06 is direct, then trains at 19:05, 20:33, and 22:37 requiring connections.

There is a way to get an earlier start and still use the Bayern ticket. Buy single journey tickets for Munich transit for 2.90 EUR pp and a Bayern Ticket. Then, you can take the 8:52 train. Your local ticket is good to Pasing, then when the train leaves Pasing, it will be 9:00 am and the Bayern Ticket is now valid for the rest of the day.

Schedule is at www.bahn.com. To go to Neuschwanstein, use "Schongau, Neuschwanstein" as destination and it will show the train and bus connections. Similar for Berchdesgaden and Koenigsee.

I should also add that the 31 EUR price is only if you buy at a ticket machine. Pay an extra 2 EUR to buy out of a ticket window. And write both your names on the back of the Bayern Ticket.
https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml?dbkanal_007=L04_S02_D002_KIN0060_REGIO-INDEX-LAENDERTICKETS-OBEN_LZ01

We visited the castles last month from Munich and used the "Pasing trick" since we already had a 3 day Munich subway pass-it worked great! Also, be aware that the tour time you request may not be anywhere close to the time you are actually assigned. I made 3 different requests before getting one that somewhat aligned with the times of transport to/from Munich. Then, when we checked in, the lady at the reservation desk didn't like what had been assigned and gave us a much better timetable to work with since we were seeing both castles and the museum. It is easy to do yourself but the logistics were a bit of a headache. For our family of 4, it was worth it to take on the planning rather than pay a whole lot more for a day tour.

We drove when we visited and were not coming from Munich. The night before our visit we stayed in nearby Reutte, Austria at Hotel Goldener Hirsch because that’s where we were when it was getting dark. An interesting owner, but the hotel was fine. Nothing much to do or see in the town itself. On the day of our visit to the castle it was so foggy we could barely see the castle standing a few feet from it.