Town to town or Plant it?

There are pros and cons. Con to planting it is time backtracking to the city you’re staying in, more daily time in trains/cars. The pro is- you unpack once always have a place to stay (no afternoons waiting for your hotel to be ready) and have more flexibility which days are bigger/longer and which are quieter. We have been looking at Nurnberg for this area as a “hub” vs stringing together 1-2 night stays.

If you’re doing many stops then you have time packing/unpacking, checking into hotels, lugging your stuff with you everywhere. But you’re also getting more time in each town and a more complete vs day visitor experience.

I think it’s valid either way.

Regarding laundry facilities, since you know where you’ll be staying, research them before going over and save them on Google maps. Just search on self service laundry and the town. If you know the word in German, type it into Google maps for the city you want to find one in. Not all towns have self service laundry facilities.

It worked well for me in Spain and I have some saved for an upcoming Scotland trip. A plus to saving the location beforehand is you can go right to it.

My wife and I seldom stay in any place more than three nights. That is generally enough time to see the town and places in the surrounding area. Years ago we spent 6 nights in Bath UK and when all was said and done, we spent about a full day driving back to Bath after visiting the sights. That wasted time could have at least been cut in half, or more, had we used two bases rather than one.

IMHO it is not reasonable to plant yourselves in any single place for all the destinations you have named. They are too far apart.

For a smaller, quieter, and more central base town in the north: consider Bad Windsheim, which is also home to perhaps the best open-air museum in Bavaria, the Franconian "Freilandmuseum." It's a former walled town with handsome old-world buildings, several good restaurants, and a spa/pool facility (known as the "Frankentherme" - which has nothing to do with Frankenstein. Franken is German for Franconia, the region to which Bamberg, Nuremberg, Rothenburg and other nice towns belong.)

https://stadt.bad-windsheim.de/fileadmin/_processed_/1/c/csm_19_11_27_Luftbild_1077b3d071.jpg

https://en.wikipedia.org/wiki/Bad_Windsheim#/media/File:Bad_Windsheim-005.jpg

https://www.tripadvisor.com/Attraction_Review-g198421-d284746-Reviews-Frankonian_Open_Air_Museum-Bad_Windsheim_Middle_Franconia_Franconia_Bavaria.html

https://www.tripadvisor.com/Attraction_Review-g198421-d1821037-Reviews-Franken_Therme_Bad_Windsheim-Bad_Windsheim_Middle_Franconia_Franconia_Bavaria.html

https://www.tripadvisor.com/Restaurants-g198421-Bad_Windsheim_Middle_Franconia_Franconia_Bavaria.html

I would look into apartments that have washing machines either inside or on site. One example:

https://www.booking.com/hotel/de/fewo-cafe-nebenan.html

In the south: Probably too late for Oberammergau... I might choose Landshut (Romantic Road town) if don't wish to compete with the tourist onslaught in Füssen. Maybe others will offer alternative suggestions.

Both Neuschwanstein and Hohenschwangau are wrongly classified as "castles" by this common but inaccurate English translation from the German (Schloß) which means "palace." For castles that are or once were real castles, you'll have to look elsewhere.