Days Fork is one of the most beautiful trails in the Wasatch, and it's one of the least trafficked. Also, from late June into early August, catch some of the most beautiful wildflowers in the entire Wasatch mountain range.
To get to the trailhead drive up Big Cottonwood Canyon to Spruces Campground. Once in the parking lot, walk to the southwest corner of the parking lot and go up the road past the bathrooms. The trailhead will be next to the overgrown baseball field.
The trail is awesome single track the whole way up to the top and never branches off so it's really easy to follow, you can't get lost. The trail trades off between steep and flat throughout the hike so it will keep your leg muscles guessing.
Once up at the top in the Days Fork basin, the trail sort of just ends. If you want to get up to the ridge line, you'll have to bush wack up the side of the basin.