Don't go via Chamonix then! It certainly awesome seeing the Alps via the route that takes you through the tunnel, but it's not quick and apart from the 'oooo what a long tunnel' thing, it ain't all that. I've been all over that area and I love it though.
Depends where you want to get to in Italy, of course. If you're looking to do it quickly, then across northern France heading towards Nancy, then Colmar, cross into Switzerland near Basel and enjoy the fast and free flowing autoroutes, then over the St Bernard Pass and it's is doable in a day if you get over the channel the night before and start fresh. You could cross into Germany for a bit of Autobahn blasting, but they can be like the A1 on a bank holiday. Germany's a secret though. It's not that expensive, the food is pretty damned good and they have a very mature attitude to speed!
On the other hand, if you want to stay in France you can cross to Italy via the Petit St Bernard which you'd get to from Geneva via Annecy, Albertville, Bourg St Maurice and takes a bit longer. Personally, I adore the Parc Naturel Regional du Queyras. Find a cheap hotel anywhere there and every road is an adventure whichever direction you take. You can reach the coast for splash in the sea at Nice, get into Italy via a number of great passes, see Monaco, ride up the Col Du Turini the most famous road on the Monte Carlo rally, see amazing ravines, ride up the Col de la Bonette, the highest road in Europe and any number of other great days out, and it's never busy. In my experience anyway.
It's a shame Switzerland is so expensive, but what I do is stay in France or Italy and make a daily raid over the border to search out those wonderful passes and return loaded with memories of fantastic roads and incredible sights.
The other bit of advice is don't expect to get much distance travelling in Northern Italy around the lakes. It's plagued with speed cameras and low speed limits and the traffic is astonishingly heavy in places. I spent an entire afternoon just getting down the north side of Lake Magiori from Belinzona to Verbania. Horrific. Best to get properly into Italy to get any miles done. The Dolomites are fantastic though, but next time I"d get there via Northern Germany and perhaps east Austria. Last time I did them.... well, here's a few pics....
http://thehandlebars.co.uk/Handlebars/Where_Eagles_Dare_trip.html
