I'm going to give an overall view of Xmas markets in the region that I've personally been to and follow up with places I've got good advice about:
Stuttgart: Yes, it's my home city so I'm biased, but if you look into my history I have recommended people don't visit or stay depending on their itinerary. For a Christmas, I think it's a must. It's absolutely one of the best in Germany - and one of the largest, but not as touristy as Nuremberg. There are two good major markets nearby, the famous Mittlealtermarkt (Middle ages market) in Esslingen and the beautiful Baroque market in Ludwigsburg, both less than 15 minute train ride from the Stuttgart Main Train Station.
Additionally there are a lot of smaller great markets easily accessible via public transit that run during this time, some of them only on weekends. I would try to avoid Stuttgart and especially Esslingen's market on Friday or Saturday evenings though as they are now crowded enough as to be unpleasant if the weather isn't awful.
I would base in Stuttgart or Esslingen for 2-3 days to enjoy the markets, tour the Ludwigsburg palace (the "Swabian Versailles") and hit the Mercedes Museum, perhaps the best auto museum in the world. Hotels are quite expensive in Stuttgart, unfortunately, but I know a lot of people who have had good experiences with AirBnB here.
Some of the other good markets in the general Neckar Valley area are Bad Wimpfen, a really lovely town with a great market, and Beitegheim-Bissingen.
Moving away:
I enjoyed Munich's diversity of markets quite a lot. This might make sense to fly into/out of. Similarly I enjoy Frankfurt and their market(s) so that's also a great city to fly in and out of and spend a couple days basing there if you go that route).
Going west:
I've not been to a single French market that really competes with a German one but Strasbroug comes close and Strasbroug is a wonderful city worth visiting on any trip. They have a gourmand market just past the "Petit France" side that is wonderful if you want to sample cookies and sausage and supposedly Beyonce's favorite gluhwein.
Colmar is a wonderful town I've taken people to many times but their market underwhelmed me. If I was going to do Alsacian markets behind Strasbourg, I'd rent a car and hit the villages. Riquewihr is the Rothenberg of Alsace and just as charming IMO.
Going south:
I've never heard anything about Baden-Baden's market. I like Freiburg but their market was really standard and kinda boring, however it's near the Ravenna Gorge market in the Black Forest which is totally worth going to if you have a car. Stunning setting and fun market.
Going east:
I mentioned Munich but it is a good market. Nuremberg is very famous, I've still yet to make it. Everyone tells me it's very crowded. Bamberg is a wonderful city with amazing beer but their market was pretty standard.
Salzburg has a pretty good market with great scenery. If you go on the right dates you can see the Krampus, which is a sight to behold. They have a great Christmas museum as well. There's also a weekend market that runs for 3 weeks at a palace, accessible outside of town by bus, that I was extremely charmed by - unique and scenic. Further south, Innsbruck is charming, has a series of smallish markets spread throughout the city, none particularly amazing, but the location of the city with easy access via public transit to a mountain makes it something to consider for winter alpine fun.
No real itinerary suggestions, but a few places to consider!