It's only 300 miles from Phoenix to Vegas, and the distance between the two along the shortest line could easily be covered in a day. However, the number of sights and the sheer variety of scenery along and around this route is simply staggering, and a leisurely drive gives an excellent introduction to America's Southwest.
Both Phoenix and Las Vegas are major transport hubs accessible by plane from all over the United States. Cars can easily be rented at either, and you can usually negotiate a free drop-off at the other end.
Flagstaff has a better range of accommodation and nightlife, but if you want to drive a little more today and a little less tomorrow, consider continuing on to Sunset Crater and Wupatki and overnighting at Cameron or Tuba City instead.
Day 2: Flagstaff to the Grand Canyon via Monument Valley
Arrive in Las Vegas in time to catch sunset over the Strip
Much of the route is in desert areas where summer heat can be fearsome and gas stations are few and far between. Take plenty of water, and fill up your tank before heading off the Interstates.
Some more info would have helped on the rents and mode of transports.
This is a usable itinerary. It explains how to get there and touches on all the major points along the way. An adventurous person could use this article, but please plunge forward and help it grow!