How much money you spend kinds depends on how much your trying to spend. Its possible to take a trip out west for incredibly cheap if you really bum it, but its also easy to blow way more money than you wanted to. I've taken two week long trips out west, one to Utah and one to Tahoe. When I wen't to Utah I think I managed to keep it under a grand for the whole week, but that was with splitting the hotel with 2 other people, and free tickets at brighton because of my season pass back east.
When I went to Tahoe, I didn't have to pay for lodging or plane tickets (I drove out, and then my parents just randomly told me they would pay for the flight back), but I easily spent at least $1500, I really have no idea how much exactly but I was pretty irresponsible with my credit cart, it was awesome and totally worth it.
The point is, its up to you. I would say at a minimum, if your going to pay for lift tickets, hotel, flights, and a rental car, its probably going to cost more than $1000. I would recommend Utah, because there is awesome public transportation, at least to LCC/BCC, not so much for the Park City area, and you don't need to rent a car. Lift tickets at PC are also a lot more expensive than those places. If you stay at the extended stay america in Sandy, the bus stops right in front of it, and a room there is like $50 a night for two double beds, a tv, a bathroom and a full kitchen.