re: Where to stop from New Orleans to Los Angeles?

Go up to Dallas, drive the State highway to Amarillo, (both good stopping points depending on the amount of hours you like to drive. You will drive past Cadillac Ranch.
LINK

There is some great bbq out there too.

Then you want to shoot over to Albuquerque, you can stop there or santa fe. Both are worth seeing. Take 40 in. I prefer I-40 to I-10 because much of that I-10 stretch is horribly boring, while I-40 gets more interesting, as the plains become desert, then mountainous desert then mountains. If you drive at night you can pull over and see more stars than you ever saw in your life, it's just so dark.
I also like 40, because it takes you near the Grand Canyon (which you need to see if you haven't) and also through the painted desert and the petrified forest.
You then take 40 into California past the Mohave and meet up with I-15 and go to LA.

This is the more scenic route and more enjoyable if you have days on your trip. The northern route also takes you close to Colorado and Las Vegas. You could actually got up to the Hoover Damn, then on to Vegas or just see the Dam and then get on I-15 into the LA.


Of course you can take I-10.
I-10 if you want speed, as you can legally average 80mph through Texas. San Antonio is a good stop. See the Alamo and the Riverwalk. I don't like El Paso, but if you are tired when you near there, you could at least say you went, I would try to soldier on to Tuscon at least. That part of New Mexico is barren, right by White Sands (the Trinity bomb site) and the only interesting thing near there may be Roswell, but even that is just a tourist trap.
Arizona is nice, Tuscon then not far away Phoenix, just not many big places to say stop, unless it was for a nice restaurant or a bar.
Then of course I-10 goes to LA.

If you want a quicker trip take ten. If you want a better road trip, go up to I-40