Austria and Germany

You could take the narrow guage train from Jenbach, just east of Innsbruck in to Zillertal which has great mountain scenery. There are several places where you can take cable cars and/or chairlifts for even better views.

Castles and mountains... Füssen, Berchtesgaden and Salzburg... I believe you answered your own question. You can get some particularly scenic views of Germany's highest peak, the Zugspitze, from Garmisch-Partenkirchen.

Driving anywhere in the Alps between Munich and Innsbruck is spectacular, you can't really go wrong. Try to make a point of seeing the Rheinfall, quite spectacular. I don't have a map with me and can't remember the name of the place that it is near maybe someone else can help me with that? There's a castle there too for the obligatory beer with great views over the waterfall.
I was personally disappointed with Neuschwanstein and it is a little out of your way. The thing I had to remind myself of when being met with a castle that ressembles something from Disney Land and all the queues to get tickets, it that it is an historic building. When I first went in 1975 I fell in love with it, no tourists or tourist shops just a beautiful castle shrouded in mist. Last year I took my children to see it and it was a disappointment. Standing in queues with hordes of others takes something of the spirit of the place away. It's perhaps worth a visit but a long drive from Munich.

We saw 3 of Ludwig- associated castles in one day and I loved the detailed interior of Neuschwanstein. would have paid more to linger longer or see more rooms. We took the carriage up the hill ( I strongly recommend) and walked down. Linderhof was a jewel. I was far less enchanted with Hohenschwangau, which was interesting from a historical perspective.
Wikipedia has an exhausting listing of castles, but be aware that some castles might not fulfill Western ideas ideas of what a 'castle' should look like.

"It's perhaps worth a visit but a long drive from Munich." Actually, it's just a little over 2 hours from Munich to Füssen by regional train and a few minutes farther by bus to Hohenschwangau. All are included, round trip, with a Bayern-Ticket, €20 for one person, €28 for up to five. For mountains, go down the Inn just into Germany, to Brannenburg, and take the cog rail Wendelsteinbahn to the top of the Wendelstein. It's not very high by Colorado standards, but in it's setting, it's pretty impressive. From the top, you can look down into the town of Bayrischzell, 3400' below. As for castles, the Festung (Fortess) in Salzburg is a real castle and pretty impressive. A ways down the Salzach, Burghausen has what they call the longest castle in Europe, still mostly intact, dating from at least the 13th century. Farther west, on the Romantic Road, the castle at Harburg is also authentic and intact.

I was personally disappointed with Neuschwanstein. Ditto that. What a rip IMHO. First you have to wait hours then see only 7 rooms or so of the place once you get in. You're roped off from wandering too. I don't know if you're a beer drinker but once you hit Munich visit the beer gardens. They're fun. And don't miss Andechs.

Castles in Austria: - Ambras, close to Innsbruck. Good armory and beautiful Renaissance fittings - Hellbrunn in Salzburg. Manneristic palace, nice park - Hohensalzburg in Salzburg. Medieval castle - Hohenwerfen, close to Salzburg. Medieval castle Castles in Bavaria: - Burghausen. Longest castle in Europe - Hohenaschau. medieval - Herrenchiemsee. Bavarian Versailles Nature in Austria:
- Small and big Ahornboden. Two picturesque valleys close to Inssbruck, full of maple trees.