Are there any good castle/hotels near Vienna and Prague? I’m looking for ones that aren’t cheesed out with tennis courts and golf courses – instead, I want ones that would give a good, you know, castle-y experience.
Failing that, any in Bavaria?
I have nothing valuable to contribute to this thread; I just wanted to say that I love your username. I’m planning on a trip to Ansbach next month to visit your namesake’s grave and the museum. 
Ccan you please elaborate? Do you want to stay in a castle (-turned-public hotel) for the castle-y experience or visit one for the castle-y experience? (I don’t know of any that have tennis courts and golf courses.)
For the “castle-castle” without the hotel near Vienna, you should visit Durnstein. You can also stay at a converted convent (sorry for the bad pun) near there.
Within Vienna, most of the “castles” tend to actually be palaces, but Schloss Belvedere, Schloss Schonbrunn and the Hofburg (main Hapsburg palace) are all “must see” if you have the time. You could stay for weeks within the inner ring and never spend a day at the same museum, church or palace (e.g. Tafelkamer, Schatzkammer (crown jewels!), Kunthitoriches (the building is art by itself, then there’s the amazing collections), Stephansdom and Karlskirche (classic churches, one of which has neat catacombs), . My wife and I went for our honeymoon last summer (just before the floods). If you happen to be out towards Salzburg, the Mirabell gardens and Schloss Hellbrunn (the water palace) are both fun, as is HohenSalzburg (the castle). Skip the sound of music tour unless you really want to go. If you go just a bit south of Salzburg by train, you can catch the best falconry show I’ve ever seen at HohenWerfen, which is a little castle garding the main pass into Salzburg. And those are just the easy castles that I can think of off the top of my head. None of them are/have been converted to hotels.
For some unsolicited advice, if you head to Austria, take advantage of the trains and public transportation. It’s so much easier than trying to deal with a car. Also, if you at least make an effort to speak German, most Austrians will happily switch to English and they love to talk. If, however, you start of with “American Tourist” they may get a little snotty, although less so than the Germans or French. All Austrian kids are required to learn English in school (since the 1970’s) but there is still a world of difference between at least trying to speak German vs just assuming they will talk to you in English.
I love Austria. It’s a great place to visit with very friendly people.