Are you planning on just someplace in the mountains? If an alternative is a possibility, although I’m not certain that there are any waterfalls, caves, or hot springs along the route, there is a walking/bicycling trail running all the way between Vienna, Austria and Passau, Germany, along the banks of the Danube. Actually, it goes farther east, to Budapest, but it sounds like you might not be heading towards Hungary. You could travel on, or along the pathway, starting in Austria and finishing up on Bavaria.
It’s paved, so I wouldn’t call it hardcore, except for how much mileage you’d want to cover over those days. We biked some of it, between Vienna and Ybbs in Austria over several days, heading west, upriver, so it was technically uphill, but easy. Walking/biking downriver instead is certainly an option. Towns along the way were welcoming, with sights, museums, and great dining, and tremendous views the whole length. If you want to move on faster at any point, the train is easy to get to for reaching the next destination.
We weren’t staying in a single place, but moving onward each day, so it was a series of one-night stays, easy to arrange as we progressed. That could be more walking/biking that you had in mind, or not in mountains with one base, but it was rewarding.