If Alsace-Lorraine is part of Germany, we're talking about a POD before 1914, but if there's an Austria to have an Anschluss with, we're talking about a POD after 1918. You should make up your mind about that.
Now if you just mean this as a thought experiment, I'd say somewhere in the south, where the milder climate allows for a longer period of outdoors activities. People don't want to go to a theme park when it's raining. So, Stuttgart, Munich or Vienna.
It's mostly a thought experiment. I hadn't come up with a fully fledged timeline as of yet. I was thinking of several scenarios and wondering where would be a good place for such a park:
1. 1871 borders: probably near Munich or Stuttgart, like you said; maybe between Lengenwang, Buchach, Steinbach, and Sulzschneid, or east of Frost in the larger Brandenburg? East of Frost could easily give you about 17.5 mi2 to use, and close to Ratiborhammer gives two sites with about 16-18 mi2 to use.
2. 1871+German Austria: Maybe Vienna, or possibly Burgenland near Wieselburg (Moson Komitat)? Between Vienna and Leopoldsdorf in Marchfelde looks promising.
3. 1871+South/New East Prussia: still Munich or somewhere in south Bavaria, Wurttemberg
4. 1871+German Austria+Lower Syria, Carniola, Trieste, Pflaum (basically, Slovenia): perhaps on Trieste, east of Kurjavici, and west of Terveis?
My concern with locating a park in Germany is all the little tiny villages that would be affected, and finding a spot where they wouldn't be.