Salt Lake City has a number of interesting free museums. Other museums that normally charge admission have free exhibits or regular free days.
The star shows and IMAX theater at the Clark Planetarium aren't free, but the planetarium does have a number of free exhibits that are interesting and worth a look, especially if you're in the area.
110 S. 400 W.
Opens at 10:30 a.m. every day
Closes following the beginning of the last show of the day, generally Sundays at 6 p.m., Mon.-Wed. at 8 p.m., Thur. at 9 p.m., Fri. and Sat. at 11 p.m.