I've been to the Xmas markets in the areas you're talking about except from Nuremberg (was going to do it this year, but we will ill so much of the time). I actually like Munich (it grows on you) but I don't think their Christmas markets are exceptional enough to stay 2 nights in a city you don't otherwise like unless you're specifically interested in Tollwood which is a unique experience.
I do adore the markets in the Stuttgart area, the big 3 which are open continuously and are all some of the best in Germany are Stuttgart, Ludwigsburg, and Esslingen, the latter being my favorite ever. But they are increasingly popular with Germans and international tourists, so I would try to schedule visits to them on weekdays. Even weekday evenings become insanely crowded if the weather is decent (i.e. not raining) and a weekend night in good weather is a nightmare. Parking is also a nightmare. Base in an AirBnB in Stuttgart or a hotel in Esslingen or another charming town on the S-Bahn line and don't think about driving to the markets.
There are a lot of other great markets in the greater Stuttgart region, but many of the best are only open for one or two weekends or one week, and a lot of them start early, so you might want to think about Thanksgiving travel, or if you plan to be around over Christmas, note that even the "big" markets often close the last Advent Sunday or on the 22nd or the 23rd and the country shuts down entirely from 24-27th. On a plus note, the French markets tend to stay open after Christmas. But if I had my druthers, I'd try to base my trip around the first week of advent for the largest selection of open markets.
I finally went to the Tuebingen Market this year, and maybe it was the drizzly weather, but I wasn't that impressed. It's unique in that it has only real handicrafts, but it's not particularly beautiful nor were the food offerings that exciting. The middle week of December hosts the real attraction, the ChocoART festival, which is like a Christmas market entirely about chocolate, basically. This is unique and worth seeing if you can make it work in your schedule, but again, go on a weekday. I went on a Friday morning and by 5pm it was becoming unreasonable.
Other great markets in the area include the Castle market at Burg Hohenzollern (one weekend only), the market at Maulbronn monastery (ditto), and Bad Wimpfen (2 weekends I believe). These are near other scenic towns and locales with markets too, so if you do some research you could hit 2 in a day, particularly with a car, from a base near Stuttgart. Train makes the timing more difficult in this case for these markets further out from the major cities. It's near impossible to visit Hohenzollern without a car, for instance, unless you're a hiker.
As for driving, if you're used to driving in snow, I wouldn't worry about it, and only once in the last 5 years have we had significant snow around Christmastime in SW Germany. You can't predict the weather, but even if it snows, Germans are efficient about clearing the major roads.
As for France, I love Strasbourg's varied markets and Colmar is always a delight. Strasbourg does have a good Park and Ride system but for your interests I'd consider basing in Colmar at a hotel at the outer ring with parking, and then walking in Colmar, taking the train to Strasbourg, and driving to villages. Outside of Colmar and Strasbourg getting around without a car can be trying in Alsace. (i know because I keep trying, lol). Hope that helps!
