After you've done a campus tour of the University of Utah, nestled adjacent to the Wasatch Mountains, you can leisurely visit the school's ample gardens and arboretum, do some hiking, or head into town for sightseeing and great dining.
The closest airport to the University of Utah is the Salt Lake City International Airport. Once on campus, you can park the rental car—the university has natural gas-powered shuttles that can take you around, with frequent pick-ups.
Be sure to set aside time to stroll through the beautiful Red Butte Garden, on the eastern edge of campus, particularly if you're visiting in the fall. This is an official arboretum of the state of Utah. Art lovers should visit the Utah Museum of Fine Arts, which is home to 5,000 years' worth of global art, spread over numerous galleries. Finally, the Natural Museum of Utah is a stunning space where you can greatly expand your earth science knowledge as well as that of Utah's Native American heritage.
It wouldn't be a visit to SLC without a stop by Temple Square, home to a massive Mormon temple. For further great architecture, visit the Salt Lake City Public Library—you can appreciate the building even if you don't go inside. If you're looking to unwind outdoors within the city limits, Liberty Park's 80 acres are a pleasant option.