If you've never been in an arid, desert-like canyon environment, be careful! You might might fall in love with solitude and desert splendor!!
In all seriousness, if a trailhead isn't within a mile of a busy overlook or visitor center, you shouldn't have to share with too many people. That, or pick a dayhike from the less visited North Rim. Of course, if you're talking about an overnighter, pick up a permit from the Backcountry Center, spend the night below the rim, and you'll get your solitude alright!!
Such a beautiful place, I would never pass up a chance to go.