I'm going to address your New Orleans to Las Vegas portion only.
You can take two paths through Texas.
Northern route through Dallas will take you through East Texas with rolling hills, small towns, and pine forests. Dallas has nice shopping, restaurants, and the 6th Floor Museum about the Kennedy assassination is very good. You can also experience some Texas Cowboy "culture" in Fort Worth half an hour from Dallas. The Dallas to Albuquerque drive is boring, but Albuquerque is a nice town with a big southwestern flare.
The Southern route which would keep you on I-10 would take you through San Antonio where there is major Mexican influence, tons of tourist attractions like the Alamo, the early Missions, and the Riverwalk. Austin is also a short drive and has wonderful live music venues, great restaurants, the Texas History Museum. New Braunsfel is also near by where you can spend a day tubbing down a beautfiul cold river. The drive from San Antonio across Texas to Tucson is long and not much in between, but you will go through the very southern end of the Rocky Mountains in very West Texas. And if you've ever wanted to drive fast legally, then this is the stretch of Highway for you. The speed limit for much of I10 past San Antonio is 85 miles an hour.
Which ever route you take, I do highly support others recommendation of goin to the Grand Canyon on your way to Vegas.