Go to a lot of places and do a lot of skiing!
Seriously though, make sure you do a lot of exploring. The mountains in Utah are obviously WAY bigger than in PA and also vary a lot more. Sure Park City has an awesome park and you'll surely want to take some laps in it, just don't get stuck there. Ski around the mountain, ski some hike-to terrain, shred Brighton, go to Snowbird, etc. and so on. If you can plan your trip so that you're skiing at a few different mountains, you will definitely get a more well rounded feel and impression for the region you're visiting.
I also think that it's fun while traveling to do some things that are unique to that area that you can't really find elsewhere. For example, if you're in PC, go visit the Olympic park and go on a bobsled ride. Go eat at the locals favorite food joint. Experience the local brews (if 21). Be friendly to everyone you meet and make some new friends.
Be open minded, be adventurous, and have fun! You can't go wrong with those three things in mind.