Monahans sand dunes in west Texas.
Other than that, not much for a buggy like yours in my area.
Pretty decent State park there though. On I-20 west of Midland/Odessa.
If you travel I-40, there are some pretty good areas just north of Amarillo on the Red River. (Edit. Canadian River)
Low flow and sand bars miles long. Lots of sand rails running there.
I'll grab some Google map pin drops and update this post.
Willow Draw Campground
State Hwy Park Rd 41, Monahans, TX 79756
https://goo.gl/maps/AWxSAtMt1kq
My bad, it's the Canadian River North of Amarillo.
River Campsite
Amarillo, TX 79108
https://goo.gl/maps/5SJYgVX3evR2