Suggestions for 3 or 4 nights

Why don't you go up to Cologne? It is a very underrated, lively city. Or you could catch the train up to Amsterdam.
I hope.you will have a car.staying 4 nights in Bacharach. While there are good B&Be there, it is pretty quiet.

I am OK with quiet. I'm in my mid 60s. Last time I was in Bacharach was 1976. Checking Rome2Rio has the train trip at 6 hrs. Too long for a 3 might stay then back to the Frankfurt area for a flight out which was why I have not considered Amsterdam.

I have thought about going to Nuremburg from Bacharach or Freiberg. Thoughts?

Ooooh, I like the Strasbourg idea!! More specifically, I think I'd spend a day in Strasbourg and then more time in one of the small towns in Alsace. It's another wine area, yes, but very different from Mosel and the Rhine. There are so many cute little half timbered villages. Colmar is interesting, but I loved the small towns like Eguisheim and Riquerwehr. There is also a fort Haut Koenigsbourg which is interesting with great views. I thought Cologne was interesting, the cathedral incredible, but relatively speaking, its all new. Sadly, Cologne was rather devastated during WWII. If you do go to Cologne, cross the love locks bridge for the views on the other side of the river.

There are so many interesting towns around Frankfurt! Marburg is one of my favorites. If you go to Friedberg, do visit the Mikvah there. It has stone steps going 25m. down to the water. Very impressive.

Other towns you might want to visit all with-in one hour train ride using the cheap local transportation - www.rmv.de
Limburg - gorgeous half-timbered houses, cathedral is very lovely
Büdingen - massive walls and towers. Rothenburg without the buses and souvenir stores
Gelnhausen - lots of half-timbered houses, church built in 1219, palace ruins from 1200's
Kronberg (nice little Staufen castle and the Johaness church has a unique, wooden barrel vaulted ceiling)
Bad Homburg - only original palace of the Kaisers, the Saalburg Roman fort, Hessen Park Open Air Museum
Idstein - lots of half-timbered houses, a witches tower, the Union church with a fabulous ceiling made of 36 oil paintings done in the style of Rubens, middle 1600's
Eltville & Eberbach monastery - Lovely little town on the Rhein with a great panaroma walk along the river with no trains. The monastery has a wonderful basilica and they produce some of the finest wines in this Rheingau area. The Name of the Rose was filmed in the interior.

In Frankfurt, visit the Senckenburg Natural History museum. If you are there on a Sat. you can visit the former Gestapo jail in the afternoon. It is called Klapperfeld. https://www.klapperfeld.de/en/opening-hours.html

Jules, if I stay in Strasbourg could I visit your suggestions as day trips? I do not want to do one night stops.

Ms. Jo, I lived in Friedberg for 2 yrs and never heard of the Mikvah. What is it? Granted my time there was when I was young and ignorant. I often visited the park below the walls and/or used the bike paths to get from one town to the next. My memory is vague of the names of the towns I actually visited. First time I ever ate a pizza that was not cut into wedges and had a raw egg on top was in a small place in Bad Nauheim. My mouth is watering when I think of the crispy chicken and awesome veal and pork dishes. Also, Germany was the first time I was introduced to a salad at the end of the meal. And the coffee and the bread and the pastries, etc, etc. Can't wait to go back.

Depends on how much driving/train travel you are willing to do in a day. While Colmar, wasn't my favorite of the Alsace towns (mostly because they are ALL very scenic), you could base there and take the train to Strasbourg. There is a lot to do in Colmar and I believe there are buses or tours to some of the smaller Alsatian towns. Colmar has some interesting museums and a very beautiful old town.

I believe mikvahs are historic ritual baths for the Jewish people. We saw one in Spain. They are interesting and some quite lovely.

The Mikvah is a ritual Jewish bath. There are several ancient ones in Germany. Like in Speyer or Worms, though the one in Worms is closed for a few years to renovate it.
http://landbote.info/mikwe/
https://www.speyer.de/sv_speyer/en/Tourism/Tourist%20attractions/Jewish%20Heritage/Ritual%20Bath%20(Mikveh)/
https://mikwe-worms.schumstaedte.de/

Thank you for the info. I would be very interested in the Mikvah and not so much in the Elvis Presley museum (mentioned in an earlier post under a different topic).
Still undecided as to destination. Given the time of year, do I dare wait until I am in country to decide?

Since all of the destinations I suggested are using local transportation, the price of the train tickets stays the same. So, you can decide that day where you want to go. This gives you time to research the towns to see what they have that interests you, check the opening times (museums are often closed on Mondays and sometimes churches too) Will they be having a fest that day you could attend?
If Büdingen interests you though, suggest booking one of the private tours offered by the TI. This tour will take you inside the massive walls and up on top of the towers. This is the only way to get inside of these structures. Price is a low 41€ I think.

Stuttgart, Tuebingen

If you plan on Nuremberg, why not Rothenberg also. It turned out to be one of my favorite towns. If you go, be sure to take the night watchman tour.

Seeing as how you are fixed on Bacharach (a great spot) and Frankfurt, and it appears you are using public transportation, I would plump for Heidelberg, a quick train ride back to Frankfurt. Speyer close by, Baden-Baden to the south, wine villages just to the west, the lovely village of Ladenburg just to the north, buses into Odenwald for hiking.

As Jo mentions, Eltville is a nice stop if you can fit it in. Up the hill, Kloster Eberbach, the restaurant has good food and a gorgeous interior.

Thanks for the suggestions. Have a bit of research to do now.