Cuda, I'm sorry, I just saw your post from the 11th. In my estimation you won't have any trouble finding rabbits in the Hobbs area. I will say that right around Hobbs it was a little grassier than it was slightly further south around Eunice. Lots of BLM/State Trust Land in both places. The jacks really liked the slightly more "open" country.
Right at the intersection of Hwy 234/Hwy 18 (on the east edge of Eunice) there is State Trust land south of 234 both east & west of 18. We saw good numbers of rabbits in those patches, and a fair amount of pigeons from a neighboring feed lot too in case you find a falcon en route from Georgia.
If you have OnX that probably does all you need/want it to, but I would look at the New Mexico Fish & Game website and study their "CarryMap" information. You can download the CarryMap app to your phone, load in the Southeast New Mexico quadrant and it'll provide you with all the BLM/State Trust, etc. maps. Further, it'll use your phone's GPS to show you where you are on the properties. it's easier to zoom/pan than my Garmin with OnX was in my opinion. It works even if you don't have cell signal, so that's not an issue.