Arizona is something like 87% public land, with lots of places to hunt.
The problem with hunting antelope here is drawing a tag. I've drawn one, and only one, and I've been applying since I was about 14 years old (I'm 43).
Also, the drawing has already been done for next fall's hunts.
Here's Arizona's G&F Dept's website:
Wyoming is probably your best bet for getting a tag. Look at their regs online, and make a call or two to their Game & Fish Dept to find out what it takes.
ETA-here's a link to Wyoming's G&F Dept:
Doe tags aren't oo hard to get in Colorado, but the date for applying for a tag for next year has passed, I think.
New Mexico might have tags available from ranchers, but they aren't cheap.