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.
There very well could be high winds and unpredictable flash flooding. Also if travelling during the day in the summer bring lots of water just in case and check your air conditioning before leaving town.
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