I stayed at Bright Angel Campground this past May for one night with my boyfriend, and I would not go back and stay there again.
The Campground its self has a beautiful setting with about 40 campsites nestled in the Grand Canyon along the bright angel creek with Phantom Ranch close by. Which offers a snack bar with beer, advance reservations for full meals, cabins or hostel style bunks, mule rides in and out of the canyon, and some shade and picnic tables to sit at and enjoy your snacks. If this is your style, I recommend trying to stay here rather than Bright Angel Campground or Cottonwood.
Major complaints being the camp sites were only about a foot apart, and other Campground users were VERY rude with their noise and super bright white headlamps at all hours of the night.
My advice is, if you are hiking through the Grand Canyon and want to camp at the bottom, skip Bright Angel and opt for Cottonwood instead. Much better spacing on campsites (and way less, maybe 10 sites total), more privacy, and you cannot tell when people at the Campground are using their headlamps for any reason, makes for a much more restful and enjoyable Grand Canyon hiking experience.