Grab a fold out map of the U.S. Draw a straight line between NY and Phoenix. Staying close to that line, pick only highways that are shown in BLUE. It is called Blue Highway Travel . I love it! It is a bit slower but using any roads BUT Interstates is a lot more fun. You should be able to complete the trip within 7-8 days easily.
first stop would be va,the second day would be little rock ak,third day would be dallas tx,fourth day would be new mexico, the evening of the fifth day ,id be over in tempe az.. if you happen to go the northern route,chances are you would be stuck in snowy mountains, your best bet would be taking the interstate 40,then once you get to az border,its real easy to get to phoenix..
If you are a AAA member ask them for the best scenic route and suggestions. If not, perhaps you should join as their service could be very necessary on the trip.Otherwise go to Mapquest.com and ask for the scenic route map and make your own plan. It wii include miles and driving times.time
Needless to say there are several choices. The following (only key points shown) has many scnenic stretches while being a direct route: Geo.Washington Bridge - I 80 - Stroudsberg, PA - I 81 South - I 78 - Harrisburg, PA - Roanoke, VA - to I 40 Tenneseee - Nashville - Little Rock - Oklahoma City - Albuquerque, NM - I 17 South - Phoenix