All three are great places...but Aspen and Vail are more expensive in both finding a place to stay/rent and tickets to ski. The information before was found in TripAdvisor.com for the second week of January, 2015. Those are round trip prices. A few more things: there are other places to ski that are close to Park City and the snow is real dry...easier to ski for us spoiled folks. Plus, Denver is the cheapest airport to fly into for Aspen/Vail but the drive can be a pain....that is completely up to you. Good luck and have a wonderful time in the US!
JetBlue.com Tripadvisor.com $233.00
JFK 8:29p▶ Nonstop▶DEN 11:06p 4h 37m
DEN 11:57p▶ Nonstop▶JFK 5:28a +1 3h 31m
US Airways TripAdvisor.com $332.00
JFK 4:58p▶ 1 stop▶SLC 10:36p 7h 38m
SLC 12:30a▶ 1 stop▶JFK 9:19a 6h 49m