In reply to Jeriqo:
I think the Arolla valley has a good mix of all this. Has some great walks and some easier alpine forays, plus huts and some sport climbing.
Cogne and pont in Italy are excellent as well through summer. There is some great walks up to huts in Cogne.
Parts of Austria are great and I really do like the dolomites.
If you want different totally, from what I hear the tatras are great, huts relatively affordable in comparison.