What would the locals do and see?

If you're in Stuttgart , whose Xmas markets are great, be sure to go to Esslingen's (Middle Ages) markets. The parade, costumed vendors, street entertainers, the stage performers make it my favorite.
Have a magical time!

There's a lot to see and do around Nuremberg, and Erlangen is basically a couple stops away by train. It's been a long time since I visited the University there, but I remember it as very bike friendly and lots of trees. The thing is you're going to be there during the holidays, and I'm not sure what you'll "see". And that's going to hold true in all the cities. I wouldn't bother to try and get to Rothenberg, but you're an easy ride to a number of cities and towns that are worth a visit.

You are going to want to check the dates of the markets for the smaller towns as you get close to the 25th this year. Many are closing on the 22nd and 23rd since Christmas is on a Friday. Big cities like Strasbourg may stay open after the 25th, but very few. Remember in Germany the 26th is also a holiday.

If you want some military history, the MM Park, just north of Strasbourg, is excellent.

The universities in Mannheim and Heidelberg are right in the city. Mannheim doesn't have the best Christmas Market, but Heidelberg's is very good, and surrounds the uni. Still, they're only a couple train stops apart.

As for deciding between Worms or Speyer I'd take Speyer any day. The Christmas market will probably be closed, but if the Technical Museum is open you don't want to miss that.

If you're leaving out of Frankfurt I'd aim to be there New Year's Eve. They should have some Christmas stuff still up, and they will have excellent fireworks. Mainz would be good too. Just remember, like Christmas, 1 JAN is a holiday and nothing will be open.

Randy,

Two thoughts come to mind. First, if you haven't studied the history of the Holy Roman Empire, I suggest some reading before the trip as many of the cities you plan to visit were ruled by the HRE. For example, in Nuremberg you can visit the Kaiserburg and tour the apartment used by the Emperor when he visited.

And second for Younger Kid, while in Colmar consider a trip to a museum focused on the Franco-Prussian war in Gravelotte https://moselle-culture.fr/site/musee-de-la-guerre-de-1870-et-de-lannexion/. There are also some battlefield sites and monuments in the area, but I don't recall the book that I read that provided the details and driving routes. I have not been to the museum as I have not worked the Alsace into my travels as of yet.

Have a great time.

Erlangen University is spread over the town

For ex the Faculty of Engineering and Technology is outside on the way to Tenenlohe and Nürnberg

The University Road is in town near the Palace and Botanic Garden
This might be a place to see

more info on visit-erlangen.de

Other places to go from Erlangen are

Bamberg 40km/40minutes north on Autobahn A73 Franken Highway :o)
and/or
the Franconian Switzerland 50km/about 1h northeast
Leave A73 in Forchheim and go on B470 towards Ebermannstadt Gössweinstein Tüchersfeld and Pottenstein
Nice countryside but I ve never been there in winter.

Frankfurt does not put on a fireworks show, it is just 1000s and 1000s of people setting off fireworks along the river and everyplace else in the city. I hate it. People are drunk, they shoot fireworks at each other, set them off in the underground stations, and it leaves a horrible mess in the city. We are hoping they ban the sale of fireworks in Germany soon. (they sell them 3 days before NYE in every store)

If you want medieval, there are some great towns near Frankfurt, like Limburg, Marburg, Büdingen, Gelnhausen, Seligenstadt, or Idstein.
Holy Roman Empire? Frankfurt was the chosen city for elections, as written in the Goldene Bulle in 1356. 30 Elections were held here, done by the 7 Electors. In the late 1500s, they had coronations here too, 10 altogether with the last one in 1796. Frankfurt was a free Imperial City too. Frankfurt is the only city to still have their own copy of the Goldene Bulle, purchased in 1372.

The Xmas market in Worms is pretty meh. Go to Speyer instead. Worms and Speyer, both have long Jewish histories if that is of interest.
Check dates for the markets in all of the cities you want to visit. Most of them end on the 22nd. Everything will shut down on the 24th by around 1400, all over Germany. The 25th and 26th are holidays and the 27th is a Sunday, but restaurants are booming and lots of museums will be open. Check their websites. Same thing on the 31st. Stores, etc. will shut down early and a lot of restaurants just won't be open. The 1st is a holiday, but museums may be open. Many restaurants are just closed for these 2 days.

Depending on how familiar you are with Germany and German university culture, you might know this already, but a few useful facts:

1. Most larger universities in Germany are spread over the whole city and do not have a campus. Campus life is just not a thing here, by and large.
2. Usually they are fairly inactive between Xmas and NY. Even faculty staff and admin are away.
3. Some unis specialize in certain subjects or general fields. Mannheim is more for economic, but not really for sciences, for example. If she were into science, I would rather recommend Darmstadt than Mannheim. If she were into humanities, neither makes much sense tbh.
4. Stuttgart has two unis, Nuremberg one

A couple of more general hints:
1. In fact, all of those places were part of the HRE. Only that some were independent within HRE, i.e. had no lord above them. Those are free and imperial cities.
2. Markets in Germany close at or before 23rd even in big cities. Only very few are open after Xmas - in that region I only know of Baden-Baden and that Strasbourg has a reduced one.
3. Strasbourg is a very nice place, actually. At least for a day trip.
4. Afaik no city does a fireworks show, it is all private people. Some older ones with historic center ban any fireworks, if that could be preferable.

If you are talking about this December for your trip, I would start booking hotels/apartments now. I booked my hotels and apartments a couple of months ago and was surprised at how many were already booked solid.

Also, when you are in Colmar, you might want to consider a day trip into Strasbourg, which is an incredible city with a breathtaking cathedral.