If you want to stay in the actual park, you need to book as far in advance as you can. The hotels book very quickly. Usually the only hotel with openings at the last minute is the hotel with no a/c and depending on when you go, you could be hating life.
We are going at the end of this month for 2 nights but staying in Williams, AZ which is a little over an hour drive. Tusayan, AZ is right outside the South Rim and depending on when you go the rates can be quite expensive.
We are doing a pink jeep 3 hour tour one day and we booked a boat tour (its just a floater not a white water rafting tour) for the following day.I booked the pink jeep tour even though it is double the cost of the one offered by the park because the jeeps go different routes and not so crammed like the bus. I chose to book in Williams, AZ because I wanted to stay on Route 66. The whole town kinda looks like Radiator Springs!
The grand canyon website is very help and the trip advisor site about the grand canyon breaks down all the hotels in the area quite well.