It's a steep descent--you'll want sturdy shoes or hiking boots and plenty of water--and you'll most likely run into other hikers. But make your way down 1.5 miles to Cedar Ridge (about an hour down and two hours back at a moderate pace), and you'll find that even the human encounters take on a different character below the rim. "This is spectacular," says Sharon Bloodgood, 65, surveying the view from Cedar Ridge with her sister and longtime hiking partner, Irene Cline, 84, both from Madison, Wis. "Mount Rainier and Lake Tahoe are pretty spectacular too," says Bloodgood, "but the sheer size of this is awesome." Solitude factor: low, but down here that doesn't seem to matter.
With the sun now overhead, it's time to head for cover. Shoshone Point doesn't show up on the park's tourist maps, making it your afternoon ace in the hole. Turn into the small roadside clearing 1.2 miles east of Yaki Point for a milelong hike along a dirt road through cool juniper forest to a permit-only picnic area near the point. Walk out onto the spectacular overlook--no guardrails here--and make your way a few dozen feet below the rim and out of sight of civilization. Solitude factor: near perfect.
There's still sunset, of course. Just for contrast, hop a free shuttle from the village to Hopi Point on the western Hermit Road, where it seems all 5 million visitors have gathered for the final show of the day. Solitude factor: Are you kidding? Watching grumpy sunsetters race for prime seats on the return bus before the sun has even dipped below the horizon, you'll be glad your earlier vistas were enjoyed more or less alone.