Park City is the only town really out of those mountains close by, so I really don't know where else you & your buds would party. Park City for a bach party, but you guys still need to find a way to get to SnowBird one day.
Also, don't know what time of year you're going... but, Park City warms up the fastest usually and could be a situation if you are going late late season. Went there a couple years ago in late March/early April, and Park City was dirty snow, and SnowBird was still a white paradise within less than 10miles.
Canyons are right next to Park City basically, so if you want to do just those 2 mountains, go Park City for the stay.