Nuremberg is a very nice German city to spend time - many interesting sights and nice pubs - but I suspect you won't have much time to enjoy it with only one day there. I like Bamberg and Regensburg very much as well but why not just stay in Nuremberg on Day 7 instead? So many good options for a day on your own in town, a little something for everyone...
Brew pubs
Kunstbunker
Rock-cut cellars
Kaiserburg (Imperial Castle
Craftsman's courtyard
DB German Train Museum
Lorenzkirche and other impressive churches/buildings
Museums
Also, I understand having an interest in WW II, but 3 of your 10 days are dominated by Nazi stuff... Dachau + 3rd Reich tour + Nazi Rally Grounds? And right after touring a concentration camp you're pulling up a chair for dinner at Hitler's old hang-out...? Seems way too dark to me.
"All suggestions welcomed!"
I think this works better:
Day 1: MUC to Füssen by train (Bayern ticket day pass); 2 nights in Füssen
Day 2: In Füssen
Day 3: Train into Munich for the day and 1 night (Bayern ticket day pass) Stow bags in a locker at the station or drop at hotel there. Do the 3rd Reich tour or whatever interests you in Munich.
Day 4: Early morning train to Dachau Bahnhof. Stow bags in locker. Catch bus to Dachau KZ. Pick up car in Dachau for your trip to Rothenburg in the afternoon. OR - if you choose to drop Dachau - you can pick up a car in Munich and spend some time in the Romantic Road towns or elsewhere on your way to R'burg. Arrive in late afternoon in Rothenburg for one night.
Day 5: AM & PM in Rothenburg (this is plenty of time for this relatively small town.) Drive to Nuremberg for 3 nights. Arrive in evening, drop car ASAP - a car in Nuremberg is mostly a handicap.
Days 6&7: In Nuremberg. Possible day trip or half-day trip.
Day 8: DB Saver Fare train ticket to Bacharach or other Rhine town, 2 nights. (St. Goar or Bingen might be better if doing a cruise; Bingen is closer to FRA as well for your departure to FRA. Try the NH Bingen hotel in Bingen, right on the river with an awesome view.
No car is needed here. Bingen shares a train line with most of the Rhine towns of interest to visitors. The line follows the river the entire way north past all the scenery as it connects all the towns - Bacharach, Oberwesel, St. Goar and Boppard all lie just to the north. Rüdesheim is directly across the river - use the passenger ferry to get there from Bingen.
Stopover on way to Rhine? Würzburg is a great choice and station has lockers.
Day 10: Catch direct 6:48 RE train (€8.50) from Bingen Rhein Hbf station to FRA airport (7:33.)