In reply to Wildabeast:
If you can afford Switzerland, there's the Breithorn half traverse, which can be done as a day trip from Zermatt. Also, Pollux normal route is a good acclimitisation option.
The Lagginhorn South Ridge is a great AD to get you going. Can be done from Hohsaas.
Zermatt/SaaS are only 2-3 hours from Cham.
There are lots of other AD options round there once you are acclimatised.