This spring I'm planning to spend 4-5 days for sport vacations. I want to go hiking and biking. I know a lot of different places in Central Europe to do that, but I'm asking here to get new hints.
The place should be in Central Europe (Austria, Germany, Switzerland, Italy, France) and should be also easy reachable by train (I'll have to take the bike with me into the train). Ideally, I should be able to start some cool hiking and biking tours (e.g. to glaciers or high mountains) directly in front of my accommodation. Obviously, the cheaper the accommodation the better, but I don't want to sleep in dorms.
Considering all these requirements, what are good places to go to?