Hello - I'll answer the questions I can and hope it helps. Mayo AZ is in a safe affluent neighborhood. Mayo does offer some options to stay on campus or near by but you may want to look into an Air BnB or VRBO for lodging. There are plenty of lyft or uber options as well as meal and grocery delivery services. Depending on where he lives - it may not be the best option location wise because you have to be nearby to go to the hospital for a deceased donor (I forget - its like 4 hours or so). Quality wise it is ranked the best in AZ.

Now to what I should have started with - If your father insurance covers mayo transplant and hospital services. Double check with his insurance and see what options you'll have. Mayo may not be covered but an adequate hospital in his location may be. This link can help https://www.srtr.org/transplant-centers/?organ=liver looking into transplant centers - you may have to copy and paste.
Remember to double check for hospital and liver transplant services - I am personally going through this and actually have to get a second insurance that covers the transplant part.

Best of luck and I wish you and your father well.