If you like the outdoors, go hiking or biking up Little or Big Cottonwood Canyon, 15-20 minutes from Salt Lake City. Millcreek and Emigration Canyonalso have great hiking and are closer to the city. Snowbird Resort in Little Cottonwood has a tram that goes to the top of the canyons, a zipline, alpine slide and rock climbing wall. Temple Square and This is the Place Heritage Park both showcase the state's Mormon heritage. If you like shopping, you can go the Gateway shopping center, which is outdoors and has a ton of stores. If you want a quick tour of downtown, the TRAX train system is free in the city's center (from the Delta Center, where the Jazz play, to the giant Grand American hotel). Note the city is currently redoing a huge downtown project, City Creek Center, so there is a lot of construction. For dinner, I would HIGHLY recommend Red Iguana, awesome Mexican food at 736 W. North Temple. Ahh Sushi at 22 E. 100 S. has really great sushi and does half-price sushi at lunch and I believe everyday from 5-6 p.m. Check out: utah.com (under "things to do" tab) and utahtrails.com for hiking. If you are going this weekend, the Utah Arts Festival runs Thursday through Sunday and it's a lot of fun!
Personal experience. Check out: utahtrails.com, utah.com (under "things to do" tab).