Tough question in many regards.  In any of your scenarios, you'll need a rental car.  Here are my comments based on my personal experiences:

Frankfurt:  Tourism - you're right, probably the least interesting of the three.  But, it does have the most variety of FKKs within easy driving distance.  Shark's is the biggest but is suffering from a bad case of upselling.  You have your choice of big clubs, small clubs and some which offer services other than those permitted under the 2017 law.  Obviously, you have to be discrete about it.  If you were make Frankfurt your destination, the primary reason would be FKKs and sex.

Berlin:  Between the 3rd Reich stuff and the communist stuff, Berlin is an absolutely fascinating city.  I've done a bunch of walking tours that meet at the Brandenburg Gate Starbucks.  You can also book a Reichstag tour - also fascinating.  It's the German equivalent to the Capitol, so you will have to bring your passport and go through security.  The downside (for me) is that the sex industry isn't very organized or anywhere near Frankfurt.  The only FKK in town is Artemis.  It's huge.  There were some lower-tier FKKs such as Airport Girls, but many simply didn't reopen after COVID.  There are also gangbangs that advertise.  I went to one a few years ago and the experience was unmemorable.

Munich:  Almost as interesting as Berlin.  If you go there, you owe it to yourself to visit Dachau.  You won't want to engage in any consenting adult activities that night.  I went to one FKK outside of town which was OK.  I'd characterize the scene somewhere between Frankfurt and Berlin.

Dusseldorf region:  This is in the German state of  North Rhine-Westphalia (NRW).  There are a variety of cities and tourist things to do.  The FKK scene is plentiful and the prices are definitely lower than Frankfurt.  Several offer non-2017 law services.  You might look at Koln, Bonn, Dusseldorf as your home base.  Please report back!

With excellent public transportation, a car is not necessary for any of the places mentioned in Frankfurt and Berlin —and both cities are great destinations otherwise.

I would think about how much you want to have a great FKK experience and how much you want to tour the country.  I live in Dallas and flights are direct to Frankfurt, so I find myself there a lot.  Once I found Sharks and Oase about three years ago, I was hooked.  I LOVE it in Frankfurt and enjoy both of those clubs so much!  I have also visited the smaller clubs Palace and Mainhatten and do like Palace for the intimacy and slower pace (also located in the city area with a shorter transit).  So, I would say you should try to make it to those in Frankfurt.  I do agree for the city, there are no real rewarding sites to see (Old Town?  *yawn*).

I have never visited the FKKs in Munich, but based on other comments it seems the experience does not match-up with Frankfurt, so visiting there should be to see sights like Dachau and maybe Hofbräuhaus too.

I recently visited FKK Globe in Switzerland and despite its popularity and raving reviews, to me it did not match-up to Sharks and Oase in Frankfurt for several reasons.

So, my recommendation is to do BOTH!  Maybe you can fly in/out of Frankfurt being a large airport and start and end your trip there?  You could spend your first day at one of the FKKs, then train or fly out to Munich or Berlin, etc. for two days, and then head back to Frankfurt for the final day at the other FKK and you get both!

For the four FKKs in Frankfurt, none have the girls sharing any facilities with the men.  Sharks and Oase both have large and nice outdoor areas with a swimming pool and food served outdoors when the weather is nice.  (Mainhatten has a pool too, but not as beautiful grounds as the others mentioned and Palace has no outdoor areas.)