score:6
First of all, I think it's going to be difficult to see all those things only using public transport. Even though public transport is quite reliable in Germany and you can get almost everywhere, it takes a lot of time. When you take a car you will be able to travel far faster. Otherwise, you will spend most of the day with traveling. You mentioned your some friends, so sharing the expense for a car should be sooo expensive. I think you will find some good bargains here on Travel SE for rental cars.
In Munich, you can easily spend two days. There are a lot of things to see, such as Frauenkirche, Marienplatz, Alter Peter, HofbrΓ€uhaus, Odeonsplatz, the Olympic Stadium and the Olympic parc, Nymphenburg, Pinakothek (the old and the new one), Karlsplatz / Stechus, Staatsoper, Viktualienmarkt and if you're there during September, the Oktoberfest is also really worth a visit.
From the tower in the Olympic park you also have a very interesting view over the city and the Olympic parc.
If your an automobile fan, you may also be interested in the BMW Welt. And if you're into soccer, you could also visit the Allianz Arena, the home of the infamous FC Bayern Munich!
The Deutsche Museum is especially interesting if you're into technical stuff. It is really worth a visit and it is the most visited museum in whole Germany. You won't be able to see everything there in one day. (On a side note, take a look at the postcards you can buy there in the souvenir shop. I'm on one of them ;)) So I would really recommend the Deutsche Museum in Munich instead the one in Spayer.
If you're into castles as you planned on your third day, you could also go to Falkenstein or Schloss HΓΆchstΓ€dt. But generally, I would recommend to focus on Neuschwanstein.
In Rothenburg there is nothing really special as far as I know, but it is just that city itself that is beautiful because it has a nice old town.
In the Black Forest you can see museums, churches and castles. You can also do some sportive activities like hiking, etc. In general, you can enjoy there the nature and the small villages. It is a more rural area. The only special things I can think of are planting mines that you can visit.
Unfortunately, I can't add anything to Herrenchiemsee castle and Kehlsteinhaus, because I've never been there.
Upvote:2
When I stayed in Munchen what I liked the most was a visit to Dachau, which was a model concentration camp during the Second World War. It is a short trip by train, and there are some guides that reunite groups in the Hauptbhanhof (main station) for the journey, for not expensive prices(I have payed around 15 euros for the train ticket plus entrance in the camp and guide accompaniance)
Upvote:4
If you want to visit mainly cities, going by trains and public transportation should be just fine (although you have to decide between cheap or fast). For visiting castles etc. in the countryside I would recommend a rental car.
I recommend Holidayautos for renting a car. It's an agency and not a rental car company. Usually you get a car from one of the big companies, but MUCH cheaper. In addition they provide stuff like unlimited mileage, CDW without extra fees, etc.
Upvote:5
In my opinion your plan is unrealistic. You are describing a very large area and you only have 6 days. If you want to focus on Bavaria alone, then anything above Nuremberg should be excluded.
Having said that, I will give my recommendations of the Franconia / Bavaria region, because it is the main one I have experience when living there.