The Green River Gorge Swimming Hole is the classic "locals" spot that is little known by outsiders. From its unmarked trailhead (find the red gate on the north side of Enumclaw Franklin Road SE) it is a short and gradual walk down to the Green River.
Once you reach the bend in the river, you'll find an established, primitive campsite and a pebbly beach that is perfect for summer campfires. More importantly, the river slows under exposed sedimentary cliff walls and creates a private, deep pool that is ideal for taking a dip and cooling off.
To experience the best views of the gorge, head 2.0 miles further northeast on Enumclaw Franklin Road SE all the way to the Bridge Overlook, where numerous creeks cascade into the 300-foot deep canyon.