I'm generally a fan of Gengenbach and the Black Forest, but your plans there for December - 14-16 Baden Baden and Blackforest(3 nights) will probably not be especially fruitful as the smaller Black Forest towns tend to be shuttered and somewhat like ghost-towns. Baden-Baden's focus on casinos and health spas is strong, if that's what you intend there, but there might be better places for indulging your stated interests in "...scenic views, Christmas markets, some castles..."
After landing at FRA, I'd be tempted to ride the direct train to Mainz am Rhein (25 minutes from FRA) for a few nights instead. Mainz has a large and lively Christmas market, lots of hotel and restaurant choices, and is a great place to visit anyway.
https://www.youtube.com/watch?v=Vf_0UKNq90w
https://www.tripadvisor.com/Attractions-g187393-Activities-Mainz_Rhineland_Palatinate.html
Mainz is a good base for a day trip or two. Castles? There are 40 of them in a 40-mile stretch of river north of Mainz. Map w/ links:
http://www.loreley-info.com/eng/rhein-rhine/castles.php
Marksburg in Braubach is an intact medieval castle open year-round for tours:
http://www.marksburg.de/en/
You can take a train down one side of the river and up the other between Mainz and Koblenz. Once you reach Bingen the scenery gets intense:
https://www.uli-franke.de/wp-content/uploads/2014/07/20140622_144833-Burg-Rheinstein.jpg
https://upload.wikimedia.org/wikipedia/commons/e/e3/Maeuseturm_Burg_Ehrenfels_Bingen_Rhein.jpg
The Rhine scenery in winter is not lush and green - stark, but still impressive. The railways hug the river bank - views are best looking across the river, so it's good to ride along both riverbanks.
http://media.gettyimages.com/photos/winter-in-bacharach-at-the-river-rhine-middle-rhine-rhineland-in-picture-id550647671
https://deeleea.com/wp-content/uploads/EUR2016-0013935.jpg
If the weather is OK, stop off in one or two towns for 1-2 hours for a walk around just to check out the old town walls and half-timbered buildings. Don't expect the towns to be lively though.
Bacharach: https://upload.wikimedia.org/wikipedia/commons/4/4c/Bacharach_BW_9.JPG
Oberwesel: http://www.oberwesel.de/en/wandern0/stadtmauerrundweg/
Rüdesheim could be a stop on this outing or done as a separate outing from Mainz. The Christmas market in this old-world wine town is very popular and for good reason.
http://w-d-n.de/en/
My daughter and I spent a couple of nights in Mainz a few years ago and very much enjoyed both the Mainz and R'heim markets, as well as the Trier Christmas market. Trier is on the border near Luxembourg and also a very worthwhile city. However, it's a long train trip from Mainz and probably for this reason not to be recommended unless your time is ample.
http://www.trierer-weihnachtsmarkt.de/en/
http://www.trier-info.de/english/sights-in-trier
Strasbourg's Christmas market is a biggie, and Strasbourg can in fact be reached in 1.3 hours from Stuttgart (rather than from Baden-Baden.)