Hoping to go skiing for a weekend next year - just H and I for my "big" birthday. Not bothered where, as long as its decent skiing, cheap and cheerful hotel and not too pricey to eat out etc. Have had a browse this morning and we can get cheap flights to Geneva but can't seem to find any cheap-ish accommodation for a weekend (2 or 3 nights).
If it's just a weekend, I would suggest one of the resorts close by like Morzine, Avoriaz, Les Gets as the are only an hour transfer.
You will probably struggle with hotels as most resorts rely on weekly bookings with a changeover at weekends (so in going for just a weekend you straddle two weeks). I would suggest you will have most luck going in low season i.e first week of the season in December or second or third week of Jan. Don't know much about hotels but do know that some property owners can be flexible and offer weekends on these flats tend to be places that are a little more out of town (we own a central flat in a ski resort and don't consider weekend lets as we would need to charge for two weeks and barely cover our costs as it is).
There is a forum called snow heads which has lots of very helpful people on who would probably be able to offer you better advice. But hope this is a little helpful.
went a couple of seasons back with skiweekends to Brides Les Bains - access to Meribel and hence 3 Valleys. It was very cheap as we went by coach but they do flights too - def recommend the company, don't remember anything bad about the weekend, even the coach wasn't that traumatic, infact now I come to think of it, it was worse getting back across London when we arrived home as half an inch of snow had totally foxed tfl! Think it was sub £200 for the weekend half board.
My friend has a small studio apartment that sleeps 2-4 in Megeve, French Alps. The weekly rate is very cheap... about 400 Euros, and close to the main cable car and town centre. Its an hour and a quarter from Geneva.