The Horton Springs Trail is deservedly one of the most popular in the area. It's one of the few trails where you will regularly pass other hikers, which is a good thing or a bad thing depending on your attitude and your level of experience. It also means that this hike is well documented in guidebooks and on maps.
To get there, take Highway 260 toward Christopher Creek. Turn left onto Tonto Creek Road. You will cross a bridge and see a well-marked parking lot on your left. Cross the road to find the Horton Springs trailhead. This is an easy hike, but a good distance of 8 miles round trip. It ends at the famous Horton Springs that gush from the side of the Rim and create a mossy, lush oasis under the trees.
Bring a water filter or plenty of water and be sure to tell someone where you are going before you leave.