Places to visit from El Paso to Corpus?

Hi everyone. I will have an opportunity to visit in a couple weeks and thought heading east from El Paso and staying close-ish to the border would be fun. I haven't made this route before and would love advice on what areas to avoid and what city might be a good place to spend the night. I will have a week or so to play with.

I will update my plans and post an ad once I have some sort of idea.

Thanks for any suggestions.

Lauryn