Nightowl,
A fine and hardy welcome to our great state! Not to brag (or maybe yes, to brag) there are not many big (or small for that matter) game animals you can't get a chance at here in Oklahoma. Some are by draw-in only, but hey still a chance. Elk, whitetail, mulies, antelope, black bear, feral hogs, Eastern/Rio Grande/Merriams turkey; we got it all.
From the southeast part of the state where they get more than 40 inches of rain a year and pine forest predominates, to the end of the panhandle where they barley average 6-8 inches a year. 200 ft above sea level to just above 5,000. Archery season from October 1 till January 15.
At least 1 public hunting area of good size in most every county. Some have several. If your into once in a lifetime, honest-to-goodness monster deer, put your name in for the McAllister Ammo plant hunt.
Big open bottomland hardwoods in the northeast, Sandy, rocky, buzzworm flats in the southwest. The foothills of the Ozarks, the Ouchita Mtns, the Kiamichi Mtns, the Wichita Mtns, Hackberry Flats, Hajek March, the Arkansas, the Candian and the Grande Rivers.
If your willing to work at it a little you will NEVER be board or without something to hunt here in Oklahoma.
Again, a big'ole welcome and good luck.
OkKeith