Help a newbie create an itinerary for Southern Germany and Austria

Very basic tip: just enter all places into Google Maps route planner and drag and drop them as long as you have a route you like. You will find it out. Likely it will not be a round trip. Consider also airport Nuremberg.

Would you rent a car for all of it or some of it? Or just stick to
trains and buses.

Often a mix makes sense. Car in Munich is not a good idea but excellent choice for countryside. Take care: cars in Austria need special sticker to use their Autobahn / motorways.

Accomodation.

In Munich I would avoid taking apartments. Lot of pressure currently on illegal landlords. Choose ho(s)tel. Apartments may "disappear" between booking and arriving.

Any great areas to bike? Any must see tours? Am I missing anything
important?

Check definitely local tourist offices. Very often they have very good recommendations. They know their region better than any guide book or forum.

"Am I missing anything important?"

Well, you have 10 days, and you have Munich and Salzburg - both of those are important places, I think, and will likely consume about half your time if you do them even a small amount of justice.

I would say that the other Rick-Steves-inspired recommendations you have picked up are quite unimportant on the whole and that they will tend to run you a bit ragged in the limited time you have.

Since you "would like to see a few great castles," I suggest avoiding Neuschwanstein (a late-19th century palace with a fake castle exterior!) which would require a full day outing from Munich with nearly 5 hours of trains and buses (all for an over-packed 30-minute tour.) To see a couple of real-article castles... you could take a short day trip by train from Salzburg out to Werfen for a visit to Hohenwerfen Castle (and falconry show.) And you can visit Hohensalzburg in Salzburg.

Palaces: There are a couple right in Munich, including Nymphenburg, which is more engaging and worthwhile than Neuschwanstein anyway. Herrenchiemsee is just off the main train line half way between Munich and Salzburg - no extra mileage needed. AS you travel between Munich and Salzburg, y ou hop off the train in Prien, stow your bags in lockers, and spend several hours there.

Hallstatt is pretty but also a big detour. Werfen is closer and its scenic location pretty wonderful. You could hike the "Sound of Music" Trail there in combination with the visit to Hohenwerfen Castle. Check out this page for trail info and other options in Werfen.

The Romantic Road isn't that scenic altogether. But the towns can be very nice. To visit a small old-world RR town look into a day trip by train from Munich to Landsberg am Lech. Maybe it's not big on Rick's list but I think the photos on this page provide convincing evidence that it's worth your time. And here is some solid information in English about Landsberg. Rick just doesn't cover everything. Like I said, it's an easy day trip by train from Munich to Landsberg - about 50 minutes each way.

And for an "important" town that you've overlooked, check out Regensburg and its UNESCO World Heritage old town center. Direct trains between Munich and Regensburg take 1.3 hours each direction.

If Dachau is truly important to you on personal grounds, OK, but keep in mind that the horrors there may haunt you for a full 24 hours afterward and render you unmotivated to enjoy yourself. Try to keep a lid on all the Nazi stuff too, lest you go home with too much of all that in your heads. After all, there are centuries of important German/European history you must completely ignore if you pack in too much pre-war and WW II stuff (Dachau, Hitler's Nest, SOM tour, Third Reich walking tour, Nazi Doc center... uggh.)

The Hitler's Nest, if you go, can be done as a day trip from Salzburg. Berchtesgaden itself is very nice and worth your time.

So with about 5 days in Munich and 5 in Salzburg, you could see both well AND take some doable day trips as I've outlined.

I largely agree with Russ, however, I strongly recommend the Romantic Road. Yes, the highway between the towns and cities are nothing spectacular, but the many towns and cites like Rothenberg on the Tauber, Dinkelsbuhel, Donauwurth, Augsburg, Oberamergau (Passion Play) and Fussen.

Salzburg is wonderful and the Eagles Nest is a very nice scenic place. Spend some time in Munich and go to the Hofbrauhaus for a beer hall experience.

What you are missing is how long it takes to get from one of these places to another. Not just the transit time of rail or car, but the getting out of a hotel, getting to transportation, getting to the next hotel, looking for parking, etc. It all eats up your days. A good guidebook would help answer many of your questions and get you thinking about other questions you haven't thought of yet.

Thank you so much for the EXTREMELY helpful information. I feel like I have a better starting off point for my research now. Much appreciated.

Maybe incorporate some mountain visits? I see you mention Zugspitze. That certainly is a destination and memorable. I just like to be near or in the mountains so might suggest exploring a train-based triangular tour taking in Munich, Innsbruck, Salzburg and back to Munich. Lots of places to stop off or stay for shorter visits. I know I am not being super specific, but you could read more in tour books about the towns and sights in this area.

We did a rail tour (not in a group) that included Vienna, Salzburg (Eagles' Nest included) Munich (Dachau included), other stops not on your list. Started and ended in Frankfurt and was about the same length, so should be reasonable to cover less miles and do everything you want. There was a company that arranged the hotels and rail and some tours along the way that we used, reasonably priced and let us customize what we wanted to see.

A brief bit of advice: Halstatt is lovely but very touristed and an outlier. The Koeningsee, right below the Eagle's Nest, has similar scenery (and yes, is similarly touristy but it's easy to get away from the crowds) and would save a bunch of time. I'd incorporate a trip to the Koeningsee to your Eagle's Nest day, take the boat ride, etc.