There's something simultaneously exhilarating, terrifying, and hypnotic about riding a camel. The lurching transition between sitting and standing is like taking on a hairy roller coaster, and camels are probably a lot taller than you realize. But once you are up and moving the swaying gait will help lull you into a contentedly sun-baked stupor, and you slide right into the timeless eternity of the desert landscape.
The desert on the west bank of Aswan is a good place to experience this for yourself. Depending on the exact route you take, you'll probably start off somewhere opposite the southern end of Elephantine Island, skirt a vivid blue and white Nubian village, and head past St Simeon Monastery—an ancient and dilapidated mud-brick structure that dates back to at least the seventh century. You'll circle back to the banks of the Nile, from where you can return to town by boat.
Like most experiences in Egypt it's easiest (though a touch more expensive) to organize this camel ride via your hotel or some other fixer. Otherwise, ask around in the bazaar or along the corniche: you'll need a boat to get you over to the west bank, a boat to bring you back, and of course your trusty camelid steed in between. Alternatively, head directly to the west bank and ask around in the villages there; just be prepared to wait if you haven't made arrangements in advance.
But however you organize your ride, don't forget to haggle!