The trailhead is located at Mueller Park, on the east bench of the city of Bountiful. It is a very popular mountain biking area. There is limited parking inside the park itself, but you can park right just outside the park on the curb and walk in. It's only about 100 yards or so to the trail. You will cross a very well maintained bridge over the creek right at the start. You will have no problems finding the trail, I mean highway. Be aware of mountian bikes as you begin to climb up the gentle switchbacks. The trail takes a westerly direction, but soon meanders back to the east as it snakes up the canyon. It ends at Rudy's Flat, a saddle north of Dude BM, on the north ridge of City Creek Canyon. It's a very pretty trail, with lots of trees and plenty of shade. There are several ridges leading down from the summit of Cave Peak, and the trail gently finds its way around these.
There is no trail to the summit of Cave Peak. After 1.70 miles, as the trail rounds a ridge, jump off the trail to the right and begin climbing the ridge. There are no signs, but you can see where someone has climbed up off the trail. You will b able to see the summit, almost 1,000 ft up and 1/2 mile away. The earlier in the spring you climb this route, the better. The brush is thick, and I'm sure by mid-summer, it will be very difficult to get through. Winter should be no problem. The brush clears out the last 200 feet or so. The summit is slightly rounded with no brush, but covered in grass. Great views extend north along the Northern Wasatch, as well as west, over the the Great Salt Lake.
It is also possible to reach the summit from North Canyon. More on this route later. See "Getting there" section for directions.
From either north or south on I-15, take exit 315. Head east on 2600 S. This road will head east, but eventually curves to the north, turning into Orchard Drive. Take a right on 1800 S., hading east. This is also known as Mueller Park Rd. Just follow this toward the mountains. It curves to the southeast, and drops down a hill to an intersection with Bountiful Blvd. Continue straight up the canyon to the TH at Mueller Park.
Follow directions for Mueller Park TH to Bountiful Blvd. Turn right (west) on Bountiful Blvd. Take your second left, and head up North Canyon. Park at the end of the road and begin climbing. Keep in mind that the mountain bikers use this area as well. More on this route later.