Your rifle should work fine. If you plan on hunting the east side, get to the range and practice out to 2-300 + yards and get very comfortable with those shots! And when you go out this fall be sure not to take shots outside of your comfort zone.
As for areas to hunt, you are in a very good central location to find critters. You can go east to Umatilla National Forest, or head north as mentioned above. You can also head north and hunt around Ellensburg. There are nice bucks to be had in both areas. There is also the private land option, which involves a lot of knocking on doors and perseverance. If you go with the last route, prepare to hear "No" a lot. But ya never know. Once you pick an area, spend as much time there as you can. The better you know the hills you are in, the better your odds will be. Find the animals, know their daily habits, and where they go when they get spooked. This will pay off opening morning when the pumpkin patch opens.
As for actually finding animals, does and smaller bucks usually aren't too hard to find. They will be spooky, but tend to hang out in relatively easy places to find and see. The bigger bucks hide well and don't move easy. I shot my largest whitetail by accidentally walking within 15 yards of a brush patch and he got spooked enough to get up and bolt. They are typically in thick nasty stuff or deep dark canyons. My success with Muleys the last few years has been credited to hiking further than most hunters are willing to go. IF you find yourself miserable and thinking about turning back, odds are most others would think the same. That's the point where I usually start finding decent bucks.
Hope this helps you out some. Hunting is by far my favorite hobby, and is super rewarding. You will get frustrated, being new. But don't let that hold you up. Nothin like walking up on your first buck!
