Well, I don't mean to speak ill of the Black Forest, it's a perfectly charming part of Germany, but I feel like it has a mythology that is built up in people's minds due to myth and reputation that doesn't quite square with the reality, especially if you're used to hiking and exploring some of the more amazing parts of the United States. The scenery is pretty and the villages charming but if you've got a week in Germany on your first trip, I'm going to recommend Berchesgadenerland over the Schwartzwald every time, tourists be damned. I also think there are villages/scenery in the Schwabish Alb that are just as stunning as anywhere in the Black Forest where you won't encounter any tourists, such as Haigerloch. It has a dramatic, cliffside setting along a rushing river. It has a palace on the dramatic hill overlooking the lower town. It has a blinged-out Baroque chapel due to it historically being part of a Catholic diocese surrounded by Protestant lands. It has the "atomkeller" where Nazi scientists worked furiously in the last days of WWII to try to create a nuclear bomb. And it's near the (way more touristy but still very impressive and historic) Hohenzollern castle.
But really, places like this abound all over Germany. Blaubeuren, not too far from Ulm, has an amazing blue pool next to an ancient monastery. The pool is the surface of a massive cave system which has some of Germany's oldest cave-dwelling remains, so there's a small but good museum to go along with that.
Or get over in Franconia and you've got another totally-off-the-trail place, Pappenheim. On the perfectly clean Altmuehl river, you paddle a canoe through woods, fields, past rock formations, charming villages, and if you don't want to hear English spoken, this is the area to go to. Hell, you won't hear German spoken, either. The Frankish dialect here is so strong that I had a pretty hard time communicating with people and my day-to-day hochdeutsch usually serves me fine. Just 45 minute train ride from Nuremberg. If paddling isn't your thing, you can also hike or bike in this wonderful region, which is also a great value. (We loved the Hotel-Gasthof Zur Sonne). There's a Jewish cemetery, a castle, and a church dating back over 850 years to see in this sleepy little town, and there's numerous small towns nearby that are equally interesting.
So what I'm saying is basically, you can find interesting, off-the-beaten path places pretty much all over Europe, it's just a matter of research. What will interest you depends on what you're looking for.