Have taken a trip to Chamonix (and beyond) a few years back, some lovely roads..
Municipal campsites in France are plentiful and good value, though we used hotels. However, we only booked the first nights accommodation, preferring to see where we ended up rather than following a fixed itinerary.
Worked well for us (it was early June when we went so there were always rooms available).
Usually, mid-afternoon we’d pull into a place we’d never heard of, check for suitable bars/cafes, then see what the local hotels were offering. Had some fab rooms at bargain prices.
The one we stopped at in Chamonix itself, Hotel de L’Avre, had a balcony over the river and a wonderful view, and only €60 back then.!
Went through the Mont Blanc tunnel and stopped to pay respects to those who’d died in the terrible fire. I’d read a story some years earlier about a tunnel guard who’d jumped on his BMW, and wearing breathing apparatus, entered several times to rescue people before succumbing himself. (Not sure how true the story is, but it was good to stop all the same).
As has been said, on the Italian side you can head for the SS26 towards the Col du Petit St Bernard, then back on the French side, the D1090 and onwards heading for the N90.. but frankly there’s so many great roads you can’t go wrong.
Oh, if heading further south, check out the Route des Grand Alps, Route Napoleon, especially the Gorge du Verdon, and I’d recommend a stop at Castellane. The Hotel du Levant is ideally situated smack bang centre of the small town..
Just take it easy, be flexible and pragmatic, you’ll have a wonderful trip I’m sure 👍
Enjoy, I’m getting itchy feet myself now.!
