The hotel is a block or two away from the Moehringen Bahnhof stop of the U-5 and U-6 so you can quickly access Stuttgart's city center from there on either U-bahn. For most of the day, U-bahns run every 10 minutes. For the Christmas Market, either the Charlottenplatz stop or the Schlossplatz stop will be right at the Christmas Market. I would recommend staying in either the City Hotel or Wirt am Berg which are in central Stuttgart and probably a similar price to the hotel you are considering. Both are a 5-10 minute walk from the Christmas Market and the Schlossplatz, and even quicker by any of the four U-bahn lines a block away. Among other ways, Stuttgart hotels are bookable through the tourist information office ( www.stuttgart-tourist.de ).
I would recommend visiting it (across from the train station on Koenigstrasse, also at the airport between baggage claims) to obtain maps and their wealth of excellent information. Make sure to get free booklets about both Esslingen ( www.esslingen.de ) and Ludwigsburg ( www.ludwigsburg.de ) if only for the maps, and although both have an English version, if they are out of them take any language just for the maps to find your way around.
If you continue on in a stop or two past the Christmas Market you will arrive at the Hauptbahnhof (main train station). Esslingen is only 15 minutes away with the S-1 and Ludwigsburg also 15 minutes away in another direction by the S-4 or S-5. From the Hauptbahnhof, Tuebingen is a little over 3/4 of an hour away. For this trip, you can use the Baden-Wuerttemberg train day ticket for a group of 2-5 for 27€. The only real restriction is no travel before 9AM on a weekday.
For traveling around Stuttgart, I believe that Möhringen is within Zone 2, so you will need a two zone group day ticket which will also get you to the TV tower, Wilhelma zoo-botanical garden, the Mercedes Benz Museum, the mineral baths, and I also believe the new Porsche Museum. Because you are staying in a hotel, you are elgible for some discounted tickets that others can't get, ask at the hotel.
For going to Ludwigsburg or Esslingen, a three zone day group ticket can be used, unless the hotel can give you a better offer with one of their special tickets.
Going to or from Tuebingen ( www.tuebingen.de ), consider stopping at Metzingen ( www.metzingen.de )which is on the way and has Germany's most factory outlets. The Tübingen Christmas Market is only for 4 days, 12-16Dec, but its a lovely town to visit even if the market isn't on.