Westward to Texas is I-10, I-12, depending on whether you go north or south of Lake Pontchartrain. They hook up together in Baton Rouge and merge as I-10.
I would guess that as soon as you get as far away as Sorrento or Ponchatoula you are pretty much OK. Slidell is toast. Covington is OK. Mandeville probably toast. Laplace could go either way.
They said TX Hwy patrol was setting up road construction outside of Houston making it worse. Dragged out a map. Looks like ~350mi between NO and Houston.