If you are just visiting for a short while, I suggest buying a cheapie prepaid Verizon phone in the last big town before you arrive (likely Flagstaff) along with some time. You may find you like the service.
I do not suggest the Verizon store as they told me with prepaid I would not get service. I went to Walmart, bought a prepaid phone and a month of service. I have full bars and my reception is fine. (FYI: I prefer pre-paid because I don't like contracts--I could qualify for a contract with any cellular provider.)
Other services may or may not work. I haven't heard of any other service working consistently. Some say ATT works, then I hear from others that ATT does not work. The Flagstaff ATT store told me it does not work in the Grand Canyon. I know that Virgin Mobile does not work because that is the service I came in with. I doubt that Sprint would work.
Another solution is most of the lodging offers free local and 800# calls. Buy a calling card before you come in, or, calling cards are available at the General store in Market Village.
Signing off from Grand Canyon, South Rim...
