Itinerary for Six Adults

Within big cities a car is definitely not a plus - public transport is faster and cheaper. If you arrive and leave in calendar month October each of you can consider D-ticket for regional and public transport in whole Germany for 63 EUR. It is a subscription; so you have to buy for October and need to cancel it until Oct 10 to avoid paying for Nov+.

For long-distance travels you need additionally separate tickets or with 6+ persons a group travel ticket. General journey planner is DB Navigator app or their website https://int.bahn.de/en.

To give you one more destination which is culturally a difference and a plus to Berlin and Munich I recommend Hamburg. With towns around such as Lübeck, Schwerin, Bremen, Stade etc. Hamburg is a great destination, all have World Heritage sites except Stade. If the ladies want to have time on their own you can park the hubbies half a day in world unique Miniatur Wunderland, but tickets need to be booked early in advance. If you need more time add the Maritime Museum and / or Ballinstadt emigration museum.

With surrounding towns / day trips I recommend Hamburg 5-6 nights, Berlin 5-6 nights, Munich 4-5. A good stop in between for 2-3 nights can be Bamberg or Nuremberg, depending on what your group likes more. I am not a fan of Rothenburg since it is over-touristic.
Special event in October in Berlin is Festival of Lights. Oktoberfest makes Munich expensive.

October 3 is national holiday.

Suggested base towns: Berlin (6 nights), Nuremberg (6 nights), Boppard (5 nights). Add days here or there if you have more time. Fly into Berlin, out of Frankfurt.

• Berlin: It's 4 days minimum here just for the city itself, IMO. You may want 7 nights for 6 days, including a day trip to Potsdam.

• Train transfer to... Nuremberg: Munich is only one of numerous great day trips by train from this city, which itself is a complete delight. Perfect base town for visiting old-world towns - Bamberg, Regensburg, (both are designated World-Heritage sites) Bad Windsheim, Iphofen, Rothenburg and others on day trips. Too many good choices!

https://www.frankentourismus.com/cities/nuremberg/
https://www.frankentourismus.com/cities/bamberg/
Iphofen... see 2 pages of photos: https://www.stadtbild-deutschland.org/forum/index.php?thread/2985-iphofen-galerie/

My thoughts here on Munich: it could be done as a day trip, or possibly two separate day trips from Nuremberg if you require extra time. Add nights to Nuremberg as needed. Sample ICE journey: 9:12 - 10:23. I assume, since you've been already, that your goal is to show your new companions what you enjoyed.

• Train transfer to... Boppard: Convenient and well-located small-town base for touring the Rhine and Mosel Valleys by train. Think also river cruises on both rivers, medieval castles everywhere, wineries, old-world villages, chairlift rides to scenic clifftop vistas, outdoor activities. Boppard has direct train connections to FRA airport.

https://www.mosel-inside.de/en/travel-guide/mosel-villages.html
https://www.mittelrheinentdecken.de/en/villages-towns-and-cities/

Another pissibility
Berlin - I have never been except at the airport. No desire to go. People seem to visit a lot of museums. How many will you want to see.

Nuremberg is good for a lot of day trips, but I stayed in a smaller town about an hour north ( Lichtenfels ) and day tripped from there.

Stay at least 1 night in Rothenburg rather than as a day trip. I think my last visit ( my 5th ) was for 4 days.

Munich - what activities do you have planned for there. I would go farther soulth to Salzburg for at least 3 nights

As a day trip from Munich, do the others want to see Neuschwanstein? You might want to rent a car so you can visit places along the way such as Wies church, Linderhof.

Trains are easy to take and will get you where you want to go. If there is somewhere not n a train route, then do a daily car rental as I suggested above.

Susan,
Trains are an option, but consider renting a vehicle for six passengers. We lived in Augsburg from 87-91 and had visitors from the USA, so we had six persons. I rented a mini-bus, it was similar to one of the 1960s VW busses. It worked out well.

Using a place as a base can work well, but if you select a large city, you much have parking to consider.

For example, if you wanted to do Berlin, you could do 4 days, just to see the City and very near places like Potsdam, then rent a bus for exploring beyond.

If you have 2-3 weeks, you could explore Berlin, Bavaria and. the Rhine Valley.
For Berlin and the area, you could just stay in Berlin.
For Bavaria, you will encounter more wasted time using Munich as a base. Visiting places like the Garmish/Fussen area would best be served by stay there for a day or two. The same with the Salzburg/Berchtesgaden area.

Rothenburg was mentioned as a base, I strongly advise against this. Staying in Rothenburg is expensive. Also, you can see that town in a day or two. I have been twice and both times we saw the entire city sites in one full day.

You might consider doing The Romantic Road, with runs from Fussen to Wurzburg, going through Augsburg and Rothenburg.

The Road includes several medieval walled towns are generally intact. Many of these towns are generally not crowded like Rothenburg or Fussen, etc. Also, it goes through Oberammergau, site of the Passion Play.

You could do the road in 3 days, I suggest overnighting in Augsburg, a scenic city that is over 2000 years old.
https://www.romanticroadgermany.com

It's not too hard to see the reason for the popularity - despite the modern roots of the idea, the tour combines the historic cities of Würzburg and Augsburg with the three medieval walled towns of Rothenburg ob der Tauber, Dinkelsbühl and Nördlingen, and then finishes off with the tourist highlights of Neuschwanstein Castle and the Alps.