Rhine Valley: I'd spend at least 2 nights here. Bingen is probably the best logistically-sound option as it's at the beginning of the most scenic section and close to FRA (1 hour) and to Frankfurt (I assume you're coming from one of those) and also closer to your Bavarian destinations than the other options to the north. Stay at the NH Bingen? It's on the mile-long river promenade and steps from the KD boat dock for your river cruise. Views are awesome.
http://www.openstreetmap.org/way/162602472#map=18/49.97017/7.89197
http://www.nh-hotels.com/nh/hotel-gallery/fachadas-16415--nh-bingen_t2-z2w.jpg
http://fischerco.de/fc/upload/objekte/Palazzo/Rheinterrasse.jpg
https://foto.hrsstatic.com/fotos/0/3/920/613/80/FFFFFF/http%3A%2F%2Ffoto-origin.hrsstatic.com%2Ffoto%2F0%2F3%2F0%2F1%2F030116%2F030116_fr_3289569.jpg/m2auv37vpQPEkfUGEgv%2FOA%3D%3D/2907,2236/6/NH_Bingen-Bingen_am_Rhein-Frhstcksraum-30116.jpg
You will want to cruise this part; Bingen - St. Goar takes 1.5 hours: http://www.bingen-ruedesheimer.com/images/map/rhine-valley290.jpg
Be sure to visit Bacharach, Oberwesel and its old town wall and St. Goar (Rheinfels Castle) which are all on the same river bank as Bingen (and easy to reach by train.)
From Bingen a passenger ferry gets you across to Rüdesheim all day long.
I'd strongly recommmend a train outing to Braubach as well - beautiful old-world town, Marksburg Castle (never-destroyed medieval castle.)
Braubach:
http://djtravel.homestead.com/files/braubach_-_hotel_1610.jpg
http://www.romantischer-rhein.de/uploads/pics/Altstadt_02.jpg
https://c1.staticflickr.com/5/4143/4751924826_36d7071291_b.jpg
About Bingen-Rothenburg-Munich... is it worth the stop in Rothenburg? Some considerations...
- Bingen-Munich can be done in 4.5 hours; stopping over in R'burg turns that into 8.5 hours on the train.
- The Rhine Valley towns offer much of the old-world, half-timbered architecture you find in Rothenburg.
- A stopover in Bamberg instead of Rothenburg can be done with 7-7.5 hours of train travel. Bamberg is a UNESCO World Heritage site - its medieval old town is uniquely well-preserved. Bamberg = beer culture. A stop of 3-4 hours might include a meal at one of Bamberg's brewery-restaurants or at least a pub visit. Here are some of Bamberg's sights
- Rothenburg is a tourist town; Rick Steves himself admits that "Rothenburg is well on its way to becoming a medieval theme park."
- You don't have much time. Munich is a lot more than Dachau. You could go straight to Munich from Bingen and still not have enough time for Munich. I wouldn't waste a full day of travel (well, 5 hours round trip) on Neuschwanstein either (fake castle exterior on a lat 19th-century palace!) All that for a 30-minute tour?? See Nymphenburg instead - it's right in Munich and there's a lot more to see.