The Canyons is the old Wolff mountain. It used to be predominantly snowbording. It IS right down the road from Park City. I have never been to the Canyons, but passed it all the time. Deer Valley is equidistant to Park City Resort, in the other direction.

Canyons was recently (last 5 years) renovated and converted to be part of the Park City Resort area and I expect it is as welcoming as both Park City and Deer Valley. Park City itself is an adorable cowboy town. There are lifts to and from the town to Park City Resort.