RF,
I'm not sure how light you are willing to camp, but the spot I used is undeveloped: barely fire circles, no picnic tables. Just parking pull-out areas. But if you are just going to park, sleep, then go, it would be ok. It is on the N. Long Jim Loop road in Tusayan. I saw the S. end of it as I drove through town, too. On the Google map, it is called Fire Road 2607. My Garmin road gps couldn't find the north end turnoff, since it has been recently changed.
Map link of turnoff. There are at least a dozen spots to park and camp. This area was practically deserted when I was there. I only saw two others camped there the afternoon I checked it out. Maybe JAGCHiker can report on how heavily it is used during the peak summer season.
You would want to then drive into the GCNP and use their huge parking lots to park your car while you are on the trail. The shuttle people would tell you the best place for parking.
I would think one day at Bright Angel campground would be about enough -- it gets hot down there, but you can play in the stream to cool off. Julius might have ideas. ...and take Julius recommendations for a super-light backpack! You DON'T need warm clothing or sleeping equipment.
If you want, I believe you can contact the concessionaire, and reserve a breakfast (5:30 and 6:30 only) at the Phantom Ranch canteen. Might make for an unusual experience.
