You probably mean the South Rim, right? That is the location almost everybody means when they say GC.
Also, which month? That matters for the weather and park access. July and August will be insanely busy.
Here's a map of the South Rim for reference. I suggest a stay at El Tovar for one night. It opened in 1905 and is a pretty kewl place. Sunrise on the South Rim is pretty spectacular. I'd also eat the the restaurant in El Tovar. Very good IMO.
If you decide to stay at ET, you'll need to make a res far in advance or check availability multiple times a day. IMHO, it's worth it. The other hotels just don't have the same history as ET, but all have a good location.
Use
THIS link to check for GC room availability.
If you're a god fearing person, and especially a catholic one,
THIS is pretty durn kewl. I think the place is kewl and I'm neither. It's in Sedona, which is < a 2 hour drive from the GC.
If you decide to go south of Phoenix, there is Saguaro Nat'l Park and the Airplane Museum/Boneyard. Both are in the Tucson area, which is a two hour drive from Phoenix.
Meteor Crater is very kewl too. And if you're an Eagles fan and want to Take it Easy, you might as well "stand on a corner in Winslow, Arizona" as it's not too far from MC.
And I'd be remiss if I did not mention Lost Wages (Las Vegas) is not far from the GC. On your drive to Vegas, you can take the dam (hoover) tour.
Good luck,
Eddie