"Cologne-Koblenz-Rhine River-Baden/Baden-Black Forest"
I'd go with this option (roughly.) You'll get lots of variety here. You'll also be in Germany's premiere castle-zone - the Rhine Valley is a UNESCO-World-Heritage site and has 40 genuine-article castles and castle ruins in just 40 miles of river. (In Füssen you'd be looking at late 19th-century palaces, not real castles.) And there'll be much less ground travel time and expense if you're leaving from Frankfurt.
I would probably dedicate 4 nights minimum to Berlin. Then a lengthy train ride to Cologne and maybe 2 nights there. That leaves 4 more. Hmmm. I'd probably discourage you from bothering with Koblenz (dull,) Baden-Baden (casinos, spas, high-end shops) and the Black Forest (pleasant but just too far.) If you spend 4 nights between the Rhine Valley and the adjacent Mosel Valley (which meets the Rhine in Koblenz,) you will have more than enough on your travel plate. I'd look into the destination options below:
Mosel options: Trier (Roman history,) Cochem (castle, falconry show, river cruises, chair lift) Burg Eltz Castle (and if you're dying for a spa, try Bad Bertrich.)
Rhine options: Marksburg Castle (Braubach,) Bacharach, Oberwesel, St. Goar (Rheinfels Castle,) Boppard, Remagen (WW II museum,) Linz am Rhein
In September there are local wine festivals every weekend in one Rhine town or another - lots of fun, often with fireworks on Saturday night. These small towns book quickly for these weekends - so book asap.
I would probably base in St. Goar on the Rhine (easy coming and going from there to all Rhine destinations) and in Cochem on the Mosel (from there, outings to Trier and Eltz are easy.) But other towns might work well too.
Cochem
Cochem Castle falconry show
Rheinfels and St. Goar
Depending on the time of your return flight, you may wish to spend your final night in a Rhine village or closer to FRA in Mainz (25 minutes by direct train to FRA.)