Take the Bright Angel Trail down to at least the 3 mile rest house and if your in good shape then Indian Garden-this is the trail that they run the mules on- -going further just commits you to hiking further out and it is a lot harder going out than going in. Past the 3 mile rest stop the elevation drops pretty fast and you still will have to get back through some areas that get very hot during the day even in early fall.
http://www.nps.gov/grca/grandcanyon/dayhike/hs_ba.htm
Not sure if they are restricting cars on the south rim right now so getting to some of the other spots may be a bit more difficult.
http://www.nps.gov/grca/grandcanyon/...r-day-hike.htm
You pretty much need to be out at least 45 minutes before sunrise and on a trail to catch that great morning light-then as the sun rises inner portions of the canyon are luminated.
BE SURE TO TAKE MORE WATER THAN YOU EXPECT- *remember as you climb out you will only be carrying back out empty bottles or an emptier bottle and a nice cool drink really will refresh you more than you realize.
I stopped at the north rim this past summer, have not been on the south rim for a few years but will never forget my hike down to the river and back on Bright Angel- If You decide that you really have to do it wait until you have been there for a couple days because, unless you are superman, you will be sore as all get out for a couple days afterwards! (if you do go this route MINIMIZE YOUR CAMERA GEAR NOT THE WATER!)