I will put my vote in for Gengenbach in the Black Forest. It's a beautiful and charming "chocolate box" town that sits right on the main train line, and it's easy to take day trips. The town itself make a great base - it's small enough not to be over-touristed and overcrowded, but it has a number of beautiful and historic sites, good hotels and very good restaurants. There's some wonderful hiking nearby and you are a short distance from other charming towns in the area, and also the Vogtsbauernhof, an open air museum that is a must-see.
And as I said, it's a good base for day trips. First, if you stay in Gengenbach, you receive a free KONUS ticket, which entitles you to free public transportation in the KONUS region, which is fairly large. In addition, the Alsace is very near - Strasbourg is a quick 30 minute trip by train.
I loved my stay in Gengenbach and would easily go back there again. Also, there are a number of castles in the vicinity, including the Hohengeroldseck Castle, Waldkirch Castle, Husen Castle, and many more.
ETA: I just noticed that you will be driving, and that's fine - I know the hotel I stayed at had facilities for parking and so do some of the others. You might want to consider getting the KONUS card anyway, since it's free, and use it for travel to places like Strasbourg, which like many other cities, is not car-friendly.