Mount Olympus is a strenuous but rewarding hike. If you have the stamina, the south summit of Mount Olympus brings you 4050 feet above the trailhead, the summit being 9026 feet in elevation. The main attractions are the great views of the valley and the experience of high alpine mountain wilderness--both available literally from the edge of Salt Lake City. Because much of the trail is south-facing, it is a good hike for dry spells during the winter.
The trail departs from a new parking lot just above Wasatch Boulevard and immediately ascends a steep stair-like section. The big rock out-crop just to the north is a popular climbing spot. The trail climbs to sections of long switchbacks, with magnificent views of Salt Lake City below. The terrain is still steep, with sections of talus slopes and rocky out-crops to negotiate. Crossing a creek bed (dry except for early spring snow melt), the trail climbs steeply through scrub oak and juniper trees to the ridge above.
Once you have made the ridge, the trail cuts its way through a different, high-alpine lifezone, where large Douglas Fir trees dominate. Scramble to the south summit, where views are stunning in all directions. Leave yourself plenty of time to rest and return down the mountain.