I'm in my 50's so not as spry as I used to be. I am just hoping to get as full a flavor of German history and culture(s) as I can.
IMHO that is something you can better accomplish without so much moving around from place to place... you are instead spending too many hours trying to cover the country geographically... there's too much time checking in and out, unpacking and repacking, and getting to and from the train stations. Too many logistics, especially if you are feeling a little low-energy.
You are flying in and out of FRA. I would instead recommend that you base yourself in no more than 3 places, including Frankfurt (there are a few good outings from Frankfurt. A few days there rather than 2 would be smart.)
Other bases I would recommend that are DIFFERENT enough that you'll get variety of culture and maybe history...
Base 2: Bacharach (well... probably not the BEST base town for several reasons, so I'll just suggest...) the Rhine Valley.
That could include Rüdesheim, Rheinfels Castle, Marksburg Castle, Oberwesel... A town closer to the Mosel River than Bacharach would be wise.... BOPPARD qualifies and is an excellent choice in its own right with many hotel and restaurant options, including many that are right beside the river. Bopppard is also a good Rhine cruise base town.
The Mosel River is beautiful and full of history too; you might catch a train, boat or bus to places like Trier, Cochem, Burg Eltz and Beilstein
Base 3: Nuremberg
Lots of history and good museums here. Good day trips too... Munich is close enough. Other good places nearby include Bamberg, Iphofen, Würzburg, and Bad Windsheim. You will be spoiled for choice. But you don't have to see them all if you aren't feeling up to it. Nuremberg itself has enough for a few days.
You'll find it very easy to move on to Frankfurt from Nuremberg - it's only a couple of hours by direct train from there.