Any question answered...

Staying in one place or moving on each day? If you do fly to Geneva then get out of Switzerland as fast as you can, as the cost of living will break the bank.

Annecy is a short distance from Geneva and offers access to some pretty amazing mountains. Aix-les-Bains/Chambery is a bit further on but from there you can access the Chartreuse massif, which has some fantastic cols in it, although none of them are higher than 1500 metres.

Further south again, Grenoble is a good option as you can ride in the Chartreuse, the Vercors to the west or the Alps proper to the south and east.

Cheers.
I've been to Switzerland a few times with work. So depressing to travel from Norway and not find everything cheaper.
Currently looking at Saint-jean-de-Mauriene area, its between Col de la Madeleine, Col de la Croix de Fer, and Alp d'huez. So plenty to chew on.