got an opportunity to take a job in 1 of 3 locations

Frisco, CO

Chakamas, OR

Flagstaff, AR

now they intention is to go to a place so i can hunt big game
specifically elk, beer and mulie
i heard that AR only does a tag drawing for hunters....is that true
and if so does anyone know if they other states are like that
money isn't a real issue but i am not looking to blow 2-3 grand if i can help it
also which states have the best herds of the three critters i mentioned and just how easy is it to get to good hunting grounds

thanks for your time and responses and good luck to all this season