From Geneva the closer resorts are in France, however you would either need a car to get there or you can get on one of the ski buses (departing from the bus station in Geneva). Ski buses often include ski passes as well. There are plenty of french resorts (Avoriaz, la Clusaz, Grand Bornard, etc) that are pretty close and fairly good for an intermetdiate level. If the bus option is too expensive (which sometimes is), you can also look for a blabla car ride.
Otherwise, if you prefer staying in Switzerland, then you will more likely get to any resort by train, but on average the ride would take more time. Verbier is amazing and steep, but it is pretty far. Otherwise there are a few resorts that can be reached from Aigle (e.g. Les Diablerets). If I am not mistaken, there are already discounts "snow&rail" or smth like that on sbb website, where you get a pack of a train ride to a resort and a ski pass - usually it is a good deal.