I know something about the northern Black Forest, having spent 23 night in four town there. Freudenstadt, mentioned by Sam, is the largest place I have stayed, for three nights. Freudenstadt was originally built around a site of a castle, that was never built, so the open area is now the town square, said to be the largest in the Germany. There is a covered walkway around most the outside of the square with lots of little shops. When I was there I stayed in a hotel facing the square, but I no longer see it listed on any site as a hotel.
I see only one three-star hotel, Krone/Arkadenhotel, shown actually facing the square. I've never stayed there, so I can't recommend it personally, but it is a three-star hotel.
There is another three-star hotel, Bären, a few block back from the square.
I've eaten, but not slept, at Hotel Schwanen. It seemed nice and it is also three-stars. It seems to me more expensive; I mention it only because it is on one of the roads leading from the Stadtbahnhof to the square, so less of a walk with luggage.
I wonder about your insistence on a three-star hotel. I never bother with stars; what's important to me is location and price. In the star-rating catalog for DEHOGA, the German Hotel and Restaurant Assoc, which issues stars, all hotels, to have even one star, have to meet the same level of cleanliness and good maintenance. What differentiates the number of stars is things like the size of the room, hours that the front desk is open, room service hours, if they have heated towel racks, or whether there is a shoe shine machine in the room. Those things mean nothing to me. I just want a clean, secure place to sleep.
In actuality, any place, with or without stars, will probably meet the cleanliness and maintenance requirements. The Germans just have high standards. I've spent many a night in a no-star hotel and never had a bad experience.
What might matter for you could be that three-star hotels are required to have someone on the staff, not necessarily always there, who speaks English. Also, any hotel with more than one star has to take credit cards. I think this fact explains why there are so many nice, un-star-rated hotels in Germany. Germans eschew credit cards, but if you don't take them, you can only have one star, so why bother.
Anyway, I found another hotel, Jägerstüble, right on the square, that looks very nice but isn't rated.
Freudenstadt is about an hour away from Gutach and the Black Forest Open-air Museum, to the south. In the other direction, Calw, the home of Steppenwolf author Hermann Hesse, with lots of Fachwerk building, would make a nice side trip.