Camping is not actually permited at the portal. Once in a while you see campers there so I guess people do sleep there. Even if you had an open truck bed to sleep in, it gets noisy there at night with cars coming and going all night. Some have laid out bags next to their car and gotten away with it...since no one usually bothers to check.
Whitney portal campsite is the closest (@7900 feet), which takes reservations. Lone Pine campground is at the bottom of the hill (@ about 6000 feet) and also takes reservations.
Tuttle creek is a little over 5000 feet, first come first serve.
If you are coming from the North, there are campsites near Independence. Some also drive the 25 miles up to Horseshoe meadows. At 10000 feet it is nice but not that close.
