Currently 124 has the highest deer harvest in the state.
Two highways will see a lot of deer coming back into Spokane during season, Hwy 395 and Hwy 2, traffic will have hunters coming back to Spokane from several GMU's, most of the biggest deer producing units in the state. You might also advertise in the local free newspapers that you need hides.
Your main competition would probably be Spokane Glove, they used to give a free pair of gloves for a deer hide, quite a few people took in their hides, not sure if they are still doing that.