The maximum permited stay at Bright Angel Campground is two nights. If you choose to stay this gives you a full day to explore. Depending on your condition there are many opportunities for things to do. These options can vary in exertion level. You might be sore from the hike down. I think the best way to help your body recover is to hike the 13 miles round trip up the North Kaibab Trail to Ribbon Falls.
Image may be NSFW.
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If you are not up for that hike there are other options. Sometimes it can be very interesting right there by the river. When the the Colorado River's flow was altered by Glen Canyon Dam in 1966 the deposition of natural sediments was halted. They have started a program of man made floods reversing this and improving conditions for wildlife in the river. Rebuilding the sandy areas is important to provide habitat for the aquatic critters. Last Sunday Nov. 18, 2012 they sent the first of many planned large floods downstream. This event was set to last for six days. Today the river flow will be returning to the man made normal and those critters will be finding new homes and making little critters. For more information about this program go here. I was in the canyon for one of three prototype high water events in November 2004. If you are interested in some background on the program go here.
Hike on past the big orange rock to see more of my photos.