In reply to tnj:
I lived in Ulm for a year. I would say go for it. As mentioned, the Blautal is really close. In summer I used to be able to get out there in the evenings after work. Tannheimer Tal just down the A7. A little bit further gets you to the Wetterstein, the mountains on the south side of Garmisch, which are great, especially the Schüsselkarspitze. The Lechtal is just a little further than the Tannheimer Tal, although I've never climbed there. The guidebook publisher Pannico has got guides to most of these areas.
Ulm is also good for getting down to Switzerland. Four hours gets you to the Furkapass. It's not quite as handy for the Dolomites and Arco since you have to go "cross country" for a stretch.
There is enough ski touring there to keep you going for years, and it's popular enough that it's really easy to get to know people to go with. Oberstdorf and Nebelhorn are probably the nearest ski resorts, and St Anton is also close enough for an easy weekend.
I'm not so much of a mountain biker, but two of my colleagues there are really keen, and I think they find enough to do.
Alex