In reply to Kimono:
Not far outside Bourg is Venosc which worked well for me as a base, at the bottom of les Deux Alpes. There's a campsite there - le champs de moulins which also rents out chalets etc. It has a nice vibe; if you bring your own bike it feels safe to keep it there and not the hassle it can be in catered accommodation. Lots and lots of Brits doing similar riding - either a plus or a minus point depending on your point of view!
St Jean de Maurienne a good sized town similar to Bourg but not as mentally cycling oriented as there worked for me.
I've also based myself at Barcelonnette, which positions itself as a tourist attraction with 6 cols for road riding. Not necessarily the big names you get in Bourg but still great fun.
All of those places have tourist accommodation in mahoosive supply. I can't comment on most of it because I slept in the campervan, but location wise I reckon any of those places will see you having a great holiday!