You really have two options. Both will probably be similar priced.
1. stay at the huntley. It'll cost 100-200 (maybe more for a bigger room? these are completely guesses but I dont think a standard room is more than 200 unless its peak times). You'll be slope side, close to bars, close to restaurants, etc. Only thing is getting from the airport to big sky, but thats like a one time shuttle fee, not too bad.
2. stay in bozeman at a dirt cheap hotel and rent a car (are you 25? if not, this will be more expensive). bozeman has tons of night life/restaurants etc and then you could ski bridger and big sky because you have transport.
Overall, i think #2 would be better. Skiing at big sky every day would be fun, but it'd get expensive. Bridger has amazing skiing and its like $50 bucks for a day ticket ($40 if you can pull out an old college id). Only thing is you'll probably fill you gas tank a few times, overall i think theyre both gonna be the same overall cost but two completely different trips. Also, for either option, ski a day at Moonlight, smaller but real fun and cheaper.