Once you reach the top of Doe Mountain, continue straight a short way on a flat trail to a cliff edge and a great viewpoint toward Sedona. From the rim, turn right and follow the rim edge along the rocky path that occasionally moves into the brush. The trail is obvious and does have some cairns along the way.
This is not a maintained trail, but is popular with locals and legal to run. As long as you work your way along the rim, you'll have great viewpoints. About 2/3 of the way, you'll reach a point that offers a perfect location to watch the sunset.
From that point, the trail meanders through manzanita bushes as you make your way back to the end of the Doe Mountain Trail #60