There are several BLM camping options near Salt Lake City. One popular spot is the Uinta-Wasatch-Cache National Forest, located about an hour's drive from Salt Lake City. Another option is the Simpson Springs campground, situated in the West Desert about 80 miles southwest of Salt Lake City. This area offers a more remote and peaceful camping experience. Keep in mind that while some BLM camping areas are free, others may require a fee for developed campgrounds.