There is plenty of skiing around Park City including the Canyons, Park City and Deer Valley (skiers only). You can also drive to Alta, Snowbird, Brighton and Sundance.
This is the main street in Park City where you will find lots of shopping and restaurants.
Plenty of other winter activities to take part in: ice skating, sledding/tubing, snowshoeing, cross-country skiing, and snowmobiling.