Ah, I used to live 15 minutes away from Bensheim in Hüttenfeld. God, how I miss that area! Will you have a car?
The Mannheim, Heidelberg, Darmstadt and Frankfurt Christmas Markets will all be going on full swing. I love the city of Heidelberg, but wasn't crazy about their market. Too discontiguous, you don't get that feeling of Weihnachtsmarkt immersion. Mannheim isn't the prettiest city, but I enjoyed their market much more. Frankfurt's is huge and occupies much of the historic Römer section of town. It looked impressive, but I didn't stay very long because my dog was a little overwhelmed by the huge crowd. Darmstadt usually goes all-out for their market, it's well worth your time. The smaller markets, like you would find in towns like Bensheim and nearby Heppenheim and Lorsch are usually open only one weekend, but try to visit one of the smaller markets if you can. Especially if you can go with a group of people you know. The real joy of the markets isn't the merchandise (which is usually rather cheap and the same everywhere), but the outdoor socializing while consuming Glühwein in a scenic atmosphere.
If you'll have a car, definitely take some time to explore the nearby Odenwald and Neckar River Valley. The Odenwald is the forested low mountain region you see immediately to the east of Bensheim... Bensheim sort of sits at the feet of the mountains. There's many scenic towns in the region, the highlights of which are probably Lindenfels (castle ruin on a hill in the middle of town, gives you a spectacular view of the area), Michelstadt (partially walled, it's medieval Rathaus usually features in German travel books that have a lot of pictures), and Erwald. The Neckar River Valley is similar to the more well-known Mittelrhein: scenic towns, and multiple castles as the Neckar River meanders through a steep valley in the Odenwald. The scenic portion runs from Heidelberg upstream to Bad Wimpfen.
Worms is pretty close to Bensheim, but despite it's long history, most of the city dates from after WWII, and isn't that attractive. If you want to see a similar city with an even more impressive Romanesque cathedral and a very pleasant Altstadt, check out nearby Speyer. With a car, the neighboring towns of Heppenheim, Weinheim and Lorsch are worth a quick visit. Don't overlook Bensheim itself, either.
Switzerland isn't as close as it looks on the map. Both driving and by train take several hours, and that only gets you to Basel and the relatively low Swiss Jura mountains. If you're looking for the Swiss Alps, you would have to procede another 45-60 minutes further to even be able to see the Alps on a clear day (which are rare in December), and another hour beyond that to actually reach them. Save Switzerland for when you have more time. The Bavarian Alps are much easier to reach from Bensheim, but still a significant distance if you only have a few days. The closest Alpine resort town is Oderstdorf. I don't know how long it takes by train, but if I timed the drive to avoid Stuttgart's rush hour, I could get there in under three hours.