I lived in Pullman while attending WSU, and did a lot of hunting and fishing around there.
My father-in-law lives in Moscow, ID (7 or so miles away), and I still get to go visiting 4 to 5 times a year, even though I now live in Seattle and it is quite a drive to Pullman (yes, upland hunting is that good!).
I can tell you from experience that in my opinion, Whitman County is one of the best spots in Washington for upland hunting - you can find a large number of pheasants, quail and partridge around the Palouse, and chukar at the river breaks. Oh yes, you can also do your waterfowling at the snake - geese and many species of ducks. There is even some doves to be had during season.
Keep in mind that you'll be less than an hour drive from the Snake River, with excellent fishing opportunities (bass, catfish, perch, sturgeon, steelhead, trout), tons of mule deer and whitetails, and rabitts.
There is also a good herd of elk nearby (Blue Mountains and Umatilla National Forest), by Asotin, and more turkeys than you'd know what to do with, both North (Colville area) and South (Clarkston) of Pullman. You can also find grouse around Clarkston.
I am sure you won't be dissapointed with the hunting opportunities should you take the job.