If you leave Los Angeles and go east on Interstate 10, you will come to a pass just east of Redlands. On the north side of the highway you will see Mount San Gorgonio (11,500 ft.) and south of the highway is Mount San Jacinto (10,804 ft.). Mt. San Jacinto is a California State Park. Here is a link to the web site.
The east side of San Jacinto is very steep and dangerous from Palm Springs. Fortunately a tram has been built to take you up to 8,500 feet at a cost of $30 per person. Here is link with more information about the tram. From the upper tram station, a six-mile trail will allow you to climb the last 2,300 feet to the top with spectacular views down to the desert below. The best time of year is very late spring when there will be water in the creeks and some snow on the trail. There will still be some snow on San Jacinto until late June even in normal precipitation years. When you are on top of San Jacinto, the most dramatic drop is on the north side of the mountain. The drop is 9,500 feet in only five horizontal miles making it one of the steepest grades in the United States.