Been A Long Time for Europe!
 

Hi everyone! It's been a long time since I have been able to travel due to life circumstances. That said, my daughter and I are taking a trip this July to several countries with limited time. We are going to Amsterdam, Prague, Munich and Annecy France. Have been to France before but always wanted to see the beautiful lake Annecy near the Alps. Thinking of eventually buying something there. However we have to cut out a day in either Amsterdam, Prague or Munich. My daughter wants to see the Neuschwanstein Castle in Munich even though it is 2 hours away in Munich. With 3 days in each place, can anyone suggest which of those 3 places to cut out a day? Would appreciate help. Would like to start booking soon. Thank you!

Question. Do you really have three whole days in each place, not counting any travel days as days in a place? That means four nights in each place.

Also, those places are quite far apart. What is your game plan for getting from place to place?

Me? I'd cut out Neuschwanstein Castle.
I take it your daughter has done no research on this trip.
Neusch isn't a castle's castle. If she's expecting a Disney experience on a tour of the castle, she'll be disappointed.
England, elsewhere in Germany, and Czech Rep have more realistic castles.
Of the four major cities you cite, the castle in Prague is far, far bigger than Neusch
Neussch had less furniture than many castles I've been in.
Honestly, when I left Neusch, I felt "is that all there is?"
I've been in perhaps 6 castles in UK, 5 in Germany, 3 in Cz Rep. 4 in France. Neusch was the least interesting, and least realistic, of the 18

That is certainly your opinion, but if this family and their daughter want to see Neuswanstein, it is up to them to decide. I found the exterior beautiful enough to see in person and would gladly see it again. While the interior is unfinished and certainly not one of the more spectacular I have ever seen, I don't, personally regret having seen it. Truly, to each their own.

How are you getting between these places? Does your 3 days in each include the travel day? If so you need a rethink. What about your arrival and departure days are they also included? These cities are so far from each other it isn't a logical collection of places to visit in such a short trip.

Most of the castle in Prague is closed to the public as it is also the seat of government. But there is the old city hall and the Strahov Monastery

https://flic.kr/p/2npmdtK https://flic.kr/p/2nprFry

You will use a minimum of one whole day of travel between each place. IMHO, your trip would be much more enjoyable by cutting, not just a day from one place, but cutting one place altogether and include seeing more in places near those you keep.
The Netherlands has so much to offer, you could easily spend more time there, plus in July, the weather “might “ be nicer.
OTOH, Germany also has a lot to see, and if Neuschwanstein is a must, consider going to Salzburg and other places in Bavaria: Garmisch and Berchtesgaden, for example. Lake Chiemsee has another of King Ludwig’s palaces, Herrenchiemsee, and you might be able to attend a concert there.

I would cut Amsterdam (since it's the most out of the way location) and save it for another trip. Add more time to Prague, and consider day trips to Cesky Krumlov - an adorable medieval village with a castle and Karlsteijn Castle, which IS like visiting a Disney castle. Just a warning though - the castle in Prague proper is beautiful on the outside, but there's not much to it on the inside. But both Karlstejn and Cesky Krumlov's castle will make up for it!