Outdoors and countryside:
Someone mentioned Rothenburg ob der Tauber earlier, which is a picturesque medieval German village in northern Bavaria. It's actually one of several towns and cities along a wonderful piece of highway the runs north and south through Bavaria known as the Romantische Straße (Romantic Road). In the summer time in particular (and then again around Christmas) this is a spectacular car trip, but I'm not sure if it's a "2 bros in a car" kind of a thing. Might be more of a "1 bro and a blond fraulein" kind of a trip.
Bodensee (Lake Constance in English) is a large Alpine lake that makes up much of the border between Germany, Switzerland and Austria. In the summer it's gorgeous, tons of outdoors activities and beautiful people. You'd want to stay at Limdau am Bodensee in Bavaria.
Innsbruck is the "Capital of the Alps" and has access to a tremendous range of outdoors activities (you stay in a hotel in Innsbruck and the city provides with you free guided hikes, for example). Everything from simple hiking to full on Alpine climbing, if it happens in the mountains it happens based out of Innsbruck. It also happens to be a terrific university town with lots of fun to be had just in the city itself. If you go, hike the Zirbenweg trail which runs between two mountain peaks (one of which was used for 2 Olympics) on the south side of the valley. It's one of the great hikes of the world and the views are beyond stunning.
The Salzkammergut is an area of lakes and hills east of Salzburg which is a UNESCO World Heritage site. It's where Habsburg and German royalty vacationed for centuries, and is truly spectacular. You can explore the whole region in a car, seeing the various castles and villages and swimming / kite surfing / boating / etc. You'd probably want to stay in Hallstatt or Bad Ischl (which is where the Habsburg "Kaiservilla" summer home is) as a base.
A little bit farther trip (you'd need to get a cheap domestic flight from Stuttgart to Hamburg) is Rügen on the Baltic coast of Germany. It's famous for it great historic beach towns and giant white cliffs. Probably comparable to a German/Scandinavian cross between Martha's Vineyard and the Hamptons, with the wildness of the maybe parts of the Carolina coast. It's a fantastic beach location. If you're in Germany in the late summer, it's definitely worth going to.
And from Stuttgart, the closest outdoors adventure is the Schwarzwald (the Black Forest). Dark wooded roads, hills, an ancient land that feels unchanged since the middle ages - that's the Black Forest. Base out of Freiburg and make sure to see Hohenzollern Castle.