Arf, iPhones....
As James said, the most convinient is Le Crozet, you can see the slopes from Geneva's city center, but as you can see, the snow isn't there at the moment.
If you have a car, you could go to one of the Portes du Soleil's resort, like Avoriaz, Les Gets or Morzine, it's about 1h15 of driving. I know well Avoriaz, it has a nice begginers area and of course the ESF (french skiing school) offers classes there. The best option is probably a group lesson for a whole day (maybe for several days if you don't have any riding experience) :
http://www.esf-avoriaz.com/en/adults/group-lessons/
Have fun !