8 days is kind of a whirlwind tour. Going much outside Munich-Salzburg-Vienna could burn a lot of your time. I guess it depends how much time you want to spend in your three highlighted cities. I think you can see highlights of Salzburg in one full day. You'll be spending a good amount on the roads. Not sure going to Nueschwanstein Castle is worth your time as it will take a day/night out of your time. From what I can read, all the rooms in the Nueschwanstein renovations are still open, you just have to deal with scaffolding and plastic sheets. Renovations will continue through 2022. I'd check before you leave. Hohenschwangau is a Schloss you could live in. It's a nice visit.
If you drive a dog leg route between Munich to Salzburg, then maybe look at Burghausen castle and old town. The castle is billed as the longest castle in the world. Overlooking the Saltzach River it is pretty impressive (border between Germany and Austria). I have never visited the rooms inside in the State Castle Museum. Plan for 3-4 hours there. https://www.burg-burghausen.de/
The Herrenchiemsee New Palace Great Hall of Mirrors is pretty fantastic. You just have to be ready to spend the time on boats to and fro and a short walk on the Island to get to the Schloss. The tours are guided and some in English. In April the gardens should be waking up. Plan for at least half a day.
