Although Dear Myrtle already posted a bit about Park City's Historical Museum, I thought I would add my $.02.
Park City makes a fun day trip from Salt Lake. The ski areas have just closed for the season, but there are still lots of fun attractions to visit. The Olympic Park has tours and rides and a fun zip line that opens May 8th, the Tanger Factory Outlet is a great place for shopping deals and Main Street is a good place to wander through art galleries and especially enjoy the nightlife. Park City is about a 40 minute drive up Parley's Canyon on the I-80 freeway.
If you go, you have to eat at Stein Erickson or Grub Steak, both pricey but absolutely legendary.