In reply to martin.p65:
Here's my tuppence-worth based on only two trips in early September.
Had some lovely weather but it also snowed, sometimes a lot : digging-ferrata-cables-out-with-your-ice-ax-at-2500m. Don't know about July but others obviously do.
I would also vote for the Brenta - it's got everything you want and is generally amazing. We used Madonna di Campiglio as a base. We didn't do any proper scrambling except Cima Faulkner - scrambly walk, very nice. But my guidebook has lots of (admittedly rather big) PDish routes doable in a day from a refuge.
Based on our trip (with added hindsight) you could take the Carlo Magno cablecar for a short less than two hours walk to the Tuckett refuge. Dump your scrambling gear, do several days hut to hut vias and return to Tuckett, pick up rope etc and do a peak or two and then lug everything back to the cablecar station. But there are limitless other possibilities. I'd think v carefully about ice axe and crampons depending on conditions and routes.
Very fond of Arabba. Super central. Loads of VFs at all levels. Village not too touristy (by local standards). Cheap accommodation.
Fanes national park was wild and looked possible for expeditions.
We found the Cicerone VF guidebooks indispensable plus they have updates on websites. For scrambling - if you can cope with Italian, "3000 delle Dolomiti" (collana vienormali) and "Cime e Alte Vie nelle Dolomiti"(tappeiner) look as if they do what they say on the tin, but I haven't tested them out yet. Also highly recommend Italian website vianormali.it, bit like an Italian camptocamp - try google translate if need be.
Have a great time. We're going back for our third September this year...