10 days in Germany

"We are fit and enjoy river/bus/train day trips... info on a couple of city home bases would be appreciated."

If you fly into FRA you can reach the Rhine River city of Mainz in around 25 minutes. Mainz is a good base for a visit to the scenic Middle Rhine Valley (castles, vineyards, old-world towns.)
http://whc.unesco.org/en/list/1066

Mainz: https://www.tripadvisor.com/Attractions-g187393-Activities-Mainz_Rhineland_Palatinate.html

Since you're fit, this is a good place for hiking/walking. Rhine Castle Trail: http://www.romantic-germany.info/index.php?id=2942

Trains cover both river banks - and you can easily get to either the east or west bank from Mainz. River boat cruises from Bingen (west bank) or Rüdesheim (east bank) to points north focus on the best part of the river for sightseeing.

http://www.bensbauernhof.com/kdboat2010a.jpg

Map of river cruise zone: https://gruppentouristik.com/sites/default/files/anbieter%202/Bingen-R%C3%BCdesheimer%20F%C3%A4hr-%20und%20Schiffahrtsgesellschaft/Rheinlauf.jpg

Castles between Bingen and Koblenz: http://www.loreley-info.com/eng/rhein-rhine/castles.php

Middle Rhine towns: http://www.loreley-info.com/eng/rhein-rhine/city-cities.php

Besides Bavaria, the Rhine of course is the classic among tourists, and also Berlin; both certainly very worthwhile seeing.

If you are feeling very adventurous, you might go to areas no other tourist has ever set foot on before you: to Northern Germany, usually blanked out in American guide books. Hamburg: great harbor town, Lübeck: lots to see, Celle: beautiful half-timbered houses, Hildesheim: UNESCO World Heritage churches, Helgoland: tiny island way out in the North Sea, Bremen: another city with lots to see, Bremerhaven: fascinating emigrant museum for all those in search of their roots.

Don't forget the Mosel, with many small cities, charming wineries, Trier, and Koblenz.

Don't miss on the East. Leipzig is wonderful, also Dresden. Both historic, with many wonderful sights. Not as touristy as Munchen. Also they are close to Poland and Prague, so a day trip to the CR or Poland is possible.

"...so prefer to pass on the SE area." Good! Now you can go to eastern and north Germany, such as Lüneburg, Weimar, Meißen, Leipzig, Minden, Münster/Westf., Eutin/Holstein, Soest, Göttingen, etc, aside from the big places Berlin, Hamburg, and Dresden. I've listed above some of the towns I've visited once or numerous times in the north and east. The tourists you might see definitely will not be American, lots of places in Germany are off the American tourist radar.

lots of places in Germany are off the American tourist radar.

We always had the feeling American guide books end at the latitude of Frankfurt, and for many, Bavaria = Germany. :-/

Not really surprising, come to think of it, with the American army bases all situated in Southern Germany. How should they know there is civilized life north of Frankfurt? ;-)

The tourists you might see definitely will not be American

There is in fact one exception to that rule. It has become quite popular among Americans to travel in search of their roots. The Northwest of Germany does get quite a few of those visitors, with the Bremerhaven emigrant museum being a main attraction of course.

I'd like to second Anna's and Fred's recommendations. Hamburg's Elbphilharmonie (concert hall) is world class and attracts tourists and music lovers in droves (concert tickets are tough to score - excuse the pun). But the access to the observation deck is free.
https://www.getyourguide.com/-l23/-tc1/?cmp=ga&campaignid=365326830&adgroupid=29642736030&targetid=aud-196325823449:kwd-1621588636&loc_physical_ms=9001461&matchtype=e&network=g&device=c&creative=190571404317&keyword=hamburg%20tours&adposition=1t3&partner_id=FDBE4&gclid=CMjSvOqVy9QCFYFqfgodzyILFw

Hamburg's Elbphilharmonie (concert hall) is world class

Yeah, once they got it finished... ;-)