In reply to Wiles:
Well seeing as you are not getting much response, I'll try to start the ball rolling.
I've not done a huge amount of Alpine rock, so others will need to give you more of a feel for say the Dolomites. Certainly that will have lots of rock routes in significant, but not huge, mountain situations, is however well known for afternoon thunderstorms in August.
A charming and not over-busy area, that tends (no guarantees given, any mountain area can fail to deliver on this, no refunds available), to have better weather, while still seeming like proper Alps is the Engandine region. Plenty of snowy peaks of not great difficulty to climb, including the classic Biancongrat on the Piz Bernina, the most easterly 4000m peak, which is a grand outing (several days involved). Usual caveats about Swiss prices apply. Not very sure about rock routes and ridges there, you would almost certainly need to look at guidebooks in German to find out.
An area of big mountains and huge uplift, many of them quite technically straightforward but well known for iffy weather (almost as bad as Chamonix!), is the Bernese Oberland. Not very sure about rock routes there, generally would not expect the rock to be very good, rather frost shattered. This is not true of the Gross Grunhorn, which has pretty sound (but razor sharp), rock on its main ridge.
So I hope that gives you something to think about and starts other people contributing.