If you want to maximize ski time and minimize cost, go to the Mounts Jura once to check it out, you to the Crozet ski station and from there you can access the others, or to St. Cergue in Switzerland, it is an small-medium sized skiing region.
you have, Crozet, Lelex-Mijoux, Les Rousses and St. Cergue ( on the Swiss side ), 50km of slopes.
You can get to Crozet from the Geneva center in 20 minutes by car, and I guess there is also a bus that goes there. it is down the mountain
From there you get the day pass ( includes the 4 mentioned ski stations ), take the lift and you are at the top of that mountain, that is where the other ski lifts are to take you to the other stations.
There are some reds and some black slopes and plenty of gentle slopes to do pownder/free ride. There is an snow park on top ( with jumps and stuff )
It is good, cheap ( 20 EUR daypass ) and near, but not huge and also as the Jura mountains are not so high ( 1600-2000 mts ) the season is shorter ( December to March only )
http://www.monts-jura.com
If you prefer the big ones and don't have a car then simply go to the "Gare Routiere" near to the place des Alpes in the morning, and take one of the ski buses, they take you to Flaîne or Avoriaz for 70 CHF per day including the transport and ski pass, you go out at 8 in the morning and come back at 5, arriving ar 6:30 to the city.