A couple years ago I went to Austin, TX for a conference. A friend went with me and we rented a car and drove back home to Oregon.
The locals in Austin told us to go to The Salt Lick. It's out of town a ways and we got lost looking for it. Once we got there, it was worth it. They don't sell alcohol, but you can bring your own. I don't think I have ever heard of a restaurant where you can bring your own?
The Salt Lick
The only place we went in New Mexico was the Carlsbad Caverns. I like them and it was a pretty drive to get there. I wanted to take I-25 north through New Mexico because I have heard it is very pretty. My friend wanted to go to San Francisco so we headed West instead. Big mistake - found out that being friends with her was a mistake too, but that's another story
I've never been anywhere else along your route, so I'm really not much help.
Good luck and have a great, safe trip!