visit as many as you can in the time your here. i'd recommend every place except deer valley. so thats park city, canyons (also in the town of park city), brighton, solitude, alta (no snowboarding), and snowbird. brighton and solitude have the least crowds. all the others can get fairly busy on the weekends.
pc has ill parks im sure you know. people hate canyons park but its way longer than pc's and i thought it was fun. brighton has endless minigolf and bigger hike/skin-to lines. solitude is small but has good/steep terrain plenty of cliffs. snowbird and alta are sick. bird has crazy vertical and both have endless terrain if you know where your traversing to.
idk where your from but out here if the trail is roped off, its closed. stay with a buddy in pow and stay in bounds if you dont know what your doing. bring your camera and have fun its something else