Okay, I think that you've got too many places on here to do in that period of time, especially since you don't want it to be too rushed. All of them are worth visiting. I would especially recommend Munich, Salzburg, and Regensburg. Bamberg is a nice and very beautiful city. I think Regensburg has a bit more substance, but that's me. Other people feel differently.
Rothenburg is great, and it's kind of the iconic German city, so it's worth a visit, but it's also a bit difficult to get to. It usually involves more than one train transfer and sometimes a bus, depending on where you're coming from.
Since you said that you don't mind renting a car, your best bet would be to start off in Munich, spend a night or two there, enough to get over jet lag, then rent a car in Munich and drive to Regensburg and stay there for two nights. From Regensburg, take a day trip to Bamberg and/or Rothenburg by driving there, which would be a whole lot easier than trying to deal with train travel. I love German trains and I always recommend them, but that area, especially when you add Rothenburg in the mix, is not conducive to easy train transfers.
From Rothenburg, you could then drive down to Salzburg. It's not too terribly long (I did it back in 2010 with a friend) and it's a really lovely and very scenic drive. You could stop in Oberammergau and some other places along the way. You could even get a look at Neuschwanstein Castle. That's what we did, although we didn't stop. I'm not that crazy about seeing the inside, but it was pretty up on the hill. Then when you leave Salzburg, you could drive straight back to Munich airport and drop off your car.
Another solution would be to drive from Rothenburg back to Munich, drop off your car there and take the train to Salzburg and spend two nights there. Then train back to Munich for your final night at the airport.
- Munich, two nights. Rent car and drive to Regensburg
- Regensburg, two nights w/day trip to Rothenburg (or 1 night Regensburg and 1 night Rothenburg)
- Drive to Salzburg, two nights.
- Drive to Munich airport and return car, one night
OR
- Munich, two nights, pick up rental car
- Regensburg, two nights w/day trip to Rothenburg (or 1 night Regensburg and 1 night Rothenburg)
- Drive to Munich, return car, train to Salzburg, two nights.
- Train from Salzburg to Munich airport - one night
I'm a little sleep-deprived, so I'm hoping this makes sense. Let me know if it doesn't.
I would definitely say don't miss Munich, definitely don't miss Salzburg, and both Regensburg and Rothenburg are well worth your time. If you want to see Bamberg, I would suggest leaving off Regensburg, but of the two, I liked Regensburg better. That's me, of course. Everyone is different, and I think Rothenburg, just by virtue of its nature as the iconic city of Germany, is well worth a short stay.
EDIT: I just realized I cheated you out of one night. According to your commentary up there, you have 8nights, so you could conceivably stay in Regensburg for two nights, which would give you time to take a day trip to Bamberg and explore Regensburg, and then also drive to Rothenburg and spend the night there on your third night or someplace in there
OR even better, in my opinion, would be to spend that third night in Salzburg. I just love Salzburg, and it's so incredibly charming and lovely. Anyway, you have a lot of options. Think it over and keep in mind that 2 nights in a city really only gives you one full day, so you don't want to deprive yourself of spending enough time in the places you choose. Sometimes you can drive yourself crazy by adding too many places in there.
