Germany - Austria

I'm not a fan of Fussen, preferring Garmisch or Mittenwald, and likewise I find Neuschwanstein to be best seen in a postcard. In October, as the leaves begin to turn, you may find a day spent between Linderhof, Ettal, and Oberammergau more attractive. But I'd also make a case for taking 2 days on the Romantic Road, because it's not a long drive and you can also stop in places like Nordlingen, or Dinklesbuhl, or Donauworth, or Augsburg. Just remember, your "Day 2" is a Sunday, and not much will be open outside of Munich (and not much there either).

I'll recommend the Boutique Hotel am Dom in Salzburg.

There isn't any way I can drive after a long flight. Lack of sleep, tiredness, jet lag, and being on unfamilar grounds are just too much. Much prefer to rent a car after getting acclimated a day or two. Perhaps you are not bothered by those things. Just food for thought.

By KGC:
"I'm not a fan of Fussen, preferring Garmisch"
I agree, Garmish is nice! The Zugspitz is right there . Any where you stay there you have a view of the ' Zug'. You can side trip to the 2 castles from there as well. Sounds like you have a car so it is very doable. The Bavarian Alps are great!
It is about a 1 hour and 15 minute drive from Munich, Fussen is almost 2 hours , maybe a little less.
Enjoy!

Love the Zugspitze near Garmisch.
Augsburg is great, its on the Romantic Road, plan at least half a day there.

The Romantic Road is great.

Will you be flying home from Munich? How long are you in Salzburg?

I could make a case for landing and taking the train directly to Salzburg first instead. No long drives after an overnight flight that way. Or alternatively, take a train to Garmisch and stay there over Fussen.

I do think it may be too much to add Romantic Road and Rothenburg. I know people love it, but we cut it for time ourselves. Feels like you want to either choose Fussen/Neuschwanstein OR Rothenburg, otherwise you’re doing a ton of driving.