Good ol' Yakima
As said, lots of options for trout. Between Yakima and Ellensburg, the Yakima River is best fished from a drift boat, but there are some places to cast from the shore. Just drive the canyon road from Selah to Ellensburg and you'll see turnout spots that look fishy. Another option is to head above Ellensburg to the stretch of the Yakima River between Ellensburg and CleEllum. There's some nice wadable water up there. Also, you can head West along Hwy 12 (White Pass) or Hwy 410 (Chinook Pass) for some smaller stream fishing. Both of these roads run parallel to rivers, and there are plenty of places to stop and fish. Nice wadable water with good (smaller) trout (although not the blue ribbon trout the Yak has). For fly shops, check out Gary's Fly Shop in Yakima (google them to find their website), or The Evening Hatch near Ellensburg along the Yakima River.
If you have wheels and don't mind driving, depending on conditions you can find Steelies on the Deschutes, Hood, or Klickitat Rivers 1.5-2 hours away from Yakima by heading South on Hwy 97. Feel free to PM me with other questions--I grew up in Yakima and can recommend restaurants, wineries, and other attractions. Enjoy your visit.