Spent a good chunk of my youth in Europe (but American, so no dog in the fight re: national pride). Traveled a lot, but never saw anything like the hike up to Neuschwanstein. There's a reason why Disney picked it. That said, I agree with those who stated that the interior was a tad lackluster. Also never been to Scotland/Wales, so can't judge there
In terms of feeling like you are living in a castle, the Weihnachtsmarkt (Christmas market) at Rothenburg ob der tauber is absolutely jaw-dropping (and not a little unlike being dropped into a Disney movie of medieval Christmas).
And the castle I'd still love to see is Hellbrunn Palace in Austria - the "water trick" castle. Can only imagine how much kids would love this:
The schloss is also famous for its jeux d'eau ("watergames") in the grounds, which are a popular tourist attraction in the summer months. These games were conceived by Markus Sittikus, a man with a keen sense of humour, as a series of practical jokes to be performed on guests. Notable features include stone seats around a stone dining table through which a water conduit sprays water into the seat of the guests when the mechanism is activated, and hidden fountains that surprise and spray guests while they take part on the tour.
https://en.wikipedia.org/wiki/Hellbrunn_Palace