Alta is 45 minutes to an hour from Park City, not because of mileage, but because part of the drive is 15 miles of winding up a two lane road in Little Cottonwood Canyon. No big deal.
There are many places to rent in Park City. Ski and See, Arcs(?), Utah Ski and Golf, the resort itself (at Legacy Lodge) and probably others I missed. Plenty of options. you probably have similar options at Deer Valley and the Canyons but PC is usually our first stop so that's where we rent.