I agree on TX, AZ, and NM as state choices. Oklahoma is a state for cats, as well. The challenge with cats, is that most states consider them furbearers with seasons and licenses. Furbearer licenses are generally pricey, as they also cover trappers, whom harvest quite a few animals.
When hunters come with me and want a bobcat, I take them to TX and don't even mess with my home state of NM. The non-res furbearer license in NM is $350. Cats are not considered furbearers in TX and you can hunt them for $48 on a temp license. I don't know what the AZ laws are on cats. I know OK has a season and the license was like $100, if I remember.
There's public land in AZ and NM, and a little bit in OK. Texas is primarly private ground.
Hope this helps...Tony
Tony