Park City has a great first day program where you can ski any of the three Park City areas for free if you have a Quick Start coupon, your boarding pass and ID.
Find details here: http://www.parkcityinfo.com/skiing/quickstart/
just click on the “click here for redemption voucher” and be sure to download this stuff before you leave for your flight.
I would head over to Deer Valley for my first day. It’s a bit farther than the ski areas in Little and/or Big Cottonwood canyons, but the skiing is free and the ticket price for Deer Valley is pretty steep. So it is a good value. Also, Deer Valley is perfect for the intermediate skier.