That should be a minimum.
Great, I have room in the itinerary to increase by another day or two.
This official NPS video of the Hermits Rest free shuttle bus route might interest you, but there are many other things to do in the park as well:
Yes but you're looking at $200 a night in those places. $100 is more our budget!
How about Motel 6 in Williams?
Can't tell from you profile what your interests are. Perhaps you could dump the expensive golf and pool time in Palm Springs and invest in some once in a lifetime quality time at the Grand Canyon.
There are budget rooms inside the GC Nat'l Park that are around $100. It's much better to stay inside the park, as opposed to Tusayan, Williams, or Flagstaff. Williams is an hour away, and Flag is a bit more. Also, read the Top Questions on the right side of the GC forum, and the NPS website: