In reply to Adderbury Climber:
The suggestion about the 'Balcony trail' on the N side of Chamonix is a good one, the paths up there by the Aiguilles Rouge are very nice and there's the scenic Lac Bleu hut up there too (excellent food) which is quite nice too. Well served by teleferiques too, you can go up from Chamonix, walk along to Lac Bleu, then either back a bit to the Flegere (or Index) tele or continue down the paths to Argentiere or even right to the end near Le Tour (frequent buses back).
Any walking up above 2600m is good acclimatisation and this area is about that, staying at the hut for a night will help too.
If you're camping there is a good one at La Praz
http://www.chamonix-camping.com/ very handy for the Flegere/Index tele or also at La Praz the excellent accomodation of La Bagna
http://chamonix-locations.com/
In Cervinia I recommend the Hotel Joli (MEUBLÉ JOLI) - lots of nice walks from there. You could also do the Breithorn from that side too, with maybe a night in the very nice Guides hut at the top of the teleferique (Rifugio Testa Grigia,3480 m) - You'll want to start your approach to the Italian ridge from halfway up this teleferique and contour around to the Abruzzi hut (being renovated I think) before heading up to the Carrell hut.
- Have a good trip!