If you are driving, there are a bunch of hotels just outside the park entrance; like Best Western, Holiday Inn, Ramada, or something like that, a little cheaper than at the canyon rim. If you want to stay in the park and don't want to spend a lot, ask about the motor lodge. Its kinda rustic and has no air conditioning, but its not too expensive either and you can walk to the canyon attractions.
You gotta go to the Arizona Room for dinner, its a steak house and it has a big picture windo so you can see the canyon at sunset. PS: if you are gonna stay at the canyon, take a flashlight. You may get caught out of your hotel at night walking from attractions, and its REAAAAAL dark there.