Germany Itinerary suggestions

Check your cruise itinerary and see if it includes an excursion to Burg Eltz. You'll be going right by it on the Mosel during your cruise.

If you want to do something after the cruise from Basel, take a train to the Berner Oberland (Wengen, Muerren) for a couple of days. Or got to Luzern for a couple of days. You could fly back from Zurich as it has a train station right at the airport.

After a lengthy transatlantic red-eye flight across 9 time zones, it's unlikely you'll emerge from FRA security and baggage ready to hop on a train for 3.5 hours. If you feel compelled to travel to Munich, then a flight into MUC would be much easier on you, and probably less expensive than a FRA flight + train.

Rick puts Munich at the top of his Germany-planning list, but there's nothing wrong with just setting his preferences out on the kitchen table to compare them with all the other options that might be nearer your cruise route.. As I understand it, you have just 6-8 days before you need to be in Luxembourg. So the Mosel destinations that your cruise misses (whichever those are) make good sense. (And the Mosel town of TRIER, curiously, isn't on your list at all.) You could say the same thing about the Rhine towns between Koblenz and Bingen (Upper Middle Rhine Valley - Boppard, St. Goar, Oberwesel, Bacharach, Braubach and others) which are on the way to Luxembourg as well - and maybe only an hour or so from FRA in some cases.

I'm looking for suggestions for sights in Munich (recommended number
of days)

I think 3 nights for Munich itself are about right. But that might be half your time, and you say you "like the small towns better than larger communities." If that's true, I would not concern myself with the time and expense of going there.

There are plenty of wonderful small towns away from the Rhine/Mosel and a lot closer to Frankfurt Airport than Munich...

Michelstadt
Miltenberg
Büdingen
Bad Wimpfen

You mention museums... Mainz and Frankfurt are both just a few minutes from FRA airport. I like Mainz especially well as a place to stay after/before a flight. Both have a nice selection of museums, shopping options, and sights - and Mainz has an especially nice tangle of streets for pedestrians only.

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

Mainz and all the other places I've mentioned are easy to reach by train - and most will completely escape your radar unless you do a little research beyond Rick Steves' limited offerings.

Other options for small-town experiences not too far from Frankfurt:

The German Half-timbered Route:
https://www.deutsche-fachwerkstrasse.de/en/Routes_Cities/From-the-River-Rhine-to-the-River-Main-and-the-Odenwald-Forest.html

The German Fairy Tale route:
https://www.deutsche-maerchenstrasse.com/en/

If you are driving back to Frankfurt from Munich, the Romantic Road is a great option. Most people know of Rothenburg ob der Tauber, but Dinkelsbuhl, Nordlingen and Donauwurth are Medieval Walled cities as well. Also, those cities are not as crowded as Rothenburg.

It's not too hard to see the reason for the popularity - despite the modern roots of the idea, the tour combines the historic cities of Würzburg and Augsburg with the three medieval walled towns of Rothenburg ob der Tauber, Dinkelsbühl and Nördlingen, and then finishes off with the tourist highlights of Neuschwanstein Castle and the Alps.

https://www.romanticroadgermany.com

If you tried to drive the Mosel Valley, that would be out of the way, since it is NW of Frankfurt. However, if you do visit Luxembourg, I suggest a stop at the small town of Vianden in NW Luxembourg.

I'm not qualified to give Bavaria advice. For the Basel end, you may find this useful for consideration:
https://community.ricksteves.com/travel-forum/switzerland/interesting-town-near-swiss-german-border

It might be possible to do Basel and Vitra Design Campus without a car, but not much else right there. Somebody said you can get to Augusta Raurica on a bus, but I had a car. Might need a vignette for Switzerland, but no problem is you rent in Basel. I think you made it clear you are flying out of Basel, rather than the more common (even with River Cruises) Zurich. You may find many of your fellow travelers are taking a cruise company bus to Zurich.

I am not tired of Cologne yet. Note that there might be wine festivals and town square tasting booths in September. Would you want to drive as far as the Black Forest (and back to return the car in the same country? Alsace is the western alternative, but you said "Germany".

My understanding was that your two 3-4-day journeys (Munich area/Romantic Road, Mosel Valley) were to be back to back, before Luxembourg and your cruise - and that you fly home out of Basel. But it looks like others might have read you differently, so I've re-read your original post a couple of times but I really can't pinpoint when your free travel periods are to take place. Do you have dates? All I see are your cruise dates.

Look at flying Icelandair. You could fly to Frankfurt, Dusseldorf, or Brussels. Or you could fly to Munich and do your drive to Trier. Fly back from Zurich.

Major European hubs from the US include Frankfurt, Munich and Zurich. If you want to go to the Munich area anyway why take a plane to Frankfurt plus train rather than just flying directly into Munich. You can train back from Munich via Nuremberg, Bamberg, Wurzburg, Frankfurt, Luxembourg, Trier to start your cruise; Or drive back via Nordlingen, Dinkelsbuh, Heidelberg, etc. After the cruise you could head to Lucerne for a few days in Switzerland. A gorgeous day trip is the Panorama Express lake steamer-train ride south over the Alps, which can conclude with a fast train back to Lucerne. Then it is an hour back to Zurich to fly home.

Have a great time!

Thank you everyone for superb suggestions. I appreciate verification of various air line hubs in Europe and will certainly take that into consideration. I also followed advice and reviewed the cruise itinerary, there is a castle tour, but it is not Burg Eltz. I'm going to try to put together a trip with the recommended cities after flying to Munich and then driving back to Frankfurt to possibly train to Luxembourg. I really appreciated the suggestions for day trips once we arrive in Switzerland. Wish me luck.

If you want to visit Burg Eltz, and you are renting a car to drive from Munich to Frankfurt, you might want to hang on to it to go to Burg Eltz, (much easier than hiking from the Moselkern train station, or being limited to a weekend when the bus is running from Hatzenport). You could turn it in in Trier, either before or after going to Luxembourg.

Rent bicycles in Munich with a route map as your guide. It’s an enjoyable and fun way to see the city.