Hi there and welcome,
There is plenty of good riding in the Jura north of Geneva. We go that way a lot, and also further down the other end of the lake in Leysin, Les Diablerets, Champery to name a few.
Still hoping to do a trip to Verbier this year, and maybe Chamonix if we get time.
For some ideas, you can check out these links:
Link1 Link2
Also, in July there is the Passportes Du soleil where you can do an 80km route (nearly all lift assisted) around Champery, Morzine, Avoriaz. Done that the last 2 years and it is a very impressive way to see a lot of places quickly, with plenty of technical riding (if like me, you prefer to keep the wheels on the ground, there are always routes around the jumps etc. the majority would be classed XC/All Mountain). Link
here.
Please post if you find some interesting routes, or shout i you fancy meeting up and doing a group ride sometime.
Cheers,
LoyalRoyal