There are elk in West Texas and panhandle. Private land only but if you can find a ranch to hunt them on the elk are there. Long Fellow ranch has a pretty large herd on it. Mulie Mike on here has a place with a small population he does a few hunts a year on. Circle K ranch has elk on it. The free range hunts are not cheap here but since they are classified exotics the license fee is small compared to out of state license prices.
There are also plenty of high fence elk across Texas.