Very nice rest area by Sierra Blanca (I believe it is)....shelters are (were anyway) in the shape of Teepees. On Westbound side, maybe Eastbound as well. Sierra Blanca a small rocky mountain, only one for miles around.
Another rest stop before getting into Van Horn, seems it is near the Time Change Sign (Mountain/Central Time Zones), also near Border Patrol Stop....after perhaps. But on the Westbound side. It has a Vista Over Look, I believe.
Just before getting to Alpine, Westbound side, a nice rest stop in a "canyon-like" area. Nice trees, small mountain/hill rocky area as I remember.
Between Alpine & West Entrance, many vistas, nice drive. Get gas in Alpine before going on.....should be less expensive.
Between Van Horn & Alpine you will find Marfa famous for being the area where the movie "Giant" was filmed and for the Marfa Lights
. Not that I have seen the Marfa lights
, never traveled in the night time along there for one reason. But remember seeing a lot of Pronghorns along the way.