Re: AZ to New Orleans
Bruce, make your way to Texline, Texas. It's right near where Texas, New Mexico and Oklahoma come together. Travel there from Raton, New Mexico on US-64 and US-87.
Then make your way to Amarillo via US-385 and I-40, but make time to stop at Cal Farley's Boys Ranch. You'll find the remainder of the old Texas town of Tascosa. It was the first 'real' Texas town in the Panhandle back during the times of the great cattle drives. Lots of history.
There's no flat country on that route, and there is a big surprise near Amarillo, too. Palo Duro Canyon. Next to the Grand Canyon it is the largest one in the USA. It ain't no gully, either! And don't forget to try your hand at eating that big state at the Big Texan in Amarillo.
Come out of Amarillo on US-287 to Wichita Falls. Don't miss looking around at Quanah. It was named after the famed Quanah Parker.
Make your way around Dallas and take I-20 to the east and visit the casinos in Shreveport, Louisiana. Maybe you'll get lucky and pay for your trip! From there you take I-49 down to Alexandria, but don't miss stopping at Natchitoches (pronounced nak-i-tish). It's a pretty neat little town. (If you're really into casinos, you can take a little side trip to the famous Coushata Casino near Kinder.)
I-49 will take you to Lafayette, Louisana at I-10. From there go east through Baton Rouge, but consider stopping there because it's the capital of Louisiana.
New Orleans is just down the road. Watch your wallet!