Utah offers a wide range of skiing opportunities. Most of the skiing surrounds Salt Lake City, readily accessible from the Salt Lake International Airport. The resorts around Salt Lake City are grouped in three different areas. Park City is located over Parley's Canyon, this is the home of Park City, Deer Valley and The Canyon's. Snowbird and Alta are located in the Little Cottonwood Canyon, while Brighton and Solitude are in the Big Cottonwood Canyon. Both the Big and Little are accessed best from I-215, follow the signs from there.
The Ogden area is home to Snowbasin and Powder Mountain. Both are worthwhile destinations. Neither have much in the way of lodging but make a good day trip from the Salt Lake Valley. Snowbasin and Powder Mountain have both been making additions in the last couple years. Of course Snowbasin's have been a bit more aggressive, the Olympic fever has struck here.
There are some other resorts scattered throughout Utah. Beaver Mountain is located in Logan Canyon. This is a Mom and Pop type operation which survives on the college students from Logan. Cheap ticket prices and fairly interesting terrain make this worth a look see. Brianhead and Elk Meadows are both located in Southern Utah. Although the snow can be rather sketchy at times, these areas provide skiing in a unique environment. High mountains in a desert plain make these areas special in their own right.
Enjoy your skiing in Utah!