did just such a trip a couple years ago, and I second what Harold1946 said.
The South Rim is best viewed by taking the bus. If you camp in either of the campgrounds inside the park, there are bus stops within an easy walk.
The North Rim is an entirely different world. Even though most Canyon visitors go only to the South Rim, you will need a reservation for the North Rim campgrounds as well. When we went, we went east to the North Rim before going on to Bryce and then Zion. I highly recommend reservations at all of them.