Yes, you can camp at the bottom of Black Canyon of the Gunnison National Park, but it requires a wilderness permit and a hike down a steep and strenuous trail. The East Portal Campground is located near the entrance of the park along the East Portal Road, which is a steep and winding road with a 16% grade. This road is drivable, not meant to be hiked. Keep in mind that the campground has limited facilities, and you should be prepared for a primitive camping experience. You can find more information about camping at Black Canyon of the Gunnison here.