I am assuming you are taking I-40 to Amarillo, then US287 to Dallas, I-20 to Shreveport, I-49 to I-10 then across to Baton Rouge.
If you like odd bits of Americana and don't mind being out in public, check out Cline Corner gas station in eastern NM, the sell everything from gas to cowboy boots, to fudge, ... Secondly Cadillac ranch west of Amarillo (bring your own spray paint and help redecorate if you so desire), also the Big Texan steak house in Amarillo. Palo Duro Canyon has already been mentioned (second largest canyon in the US).
Beyond that not a lot worth mentioning along the route, various small towns, though none that really stand out as must stops. Natchitoches, Louisiana (pronounced NAK-ca-tosh) about 75 miles south of Shreveport on I49 has an major annual Christmas lights festival https://www.natchitocheschristmas.com/
In the food department while passing through cajun country make sure to stop and get some authentic cajun food, along this route I would suggest Pats on the Wharf in Henderson, (don't stop at the fake cajun Landry's in Henderson, they are based out of Houston, TX, and were founded in Katy, TX) Pat's is about a 5 mile drive down a side highway that parallels I-10, but worth it, and if you get there outside prime hours there should be room to park an RV in the parking lot (overflow parking in the back at the second parking lot entrance by the motel).
Pat's Fisherman's Wharf Restaurant | Henderson, LA