From the North Trailhead, take the Blue Trail up to the South Rim. The first two miles are mostly up with some moderate climbs. About a mile in, take a moment to view the Shackleford Overlook. This gives you a view of the highest point in the park.
At around 1.5 miles, the trail reaches the South Rim. There's only a small climb left with a long gradual descent to Peavine Falls. Along the way, there are several side trails leading to overlooks from the south side of Double Oak Mountain. Eventually, the Blue Trail passes close by the top of Peavine Falls. Take a side trail to view the Falls from the top or another trail leading to the bottom. The Blue Trail ends at its connection with the White Trail