Spokane. For easy hiking.
Dishman hills natural area
Go out Appleway (Sprague exit). (if you can't find it, just google Dishman Dodge dealership). Just past the dodge dealer, on the right hand side (if you are coming from the west) some wooded foothills. There are some great trails there, considering they are basically in city limits. Several neat miles of wooded trails, some with great views of the valley.
(I can't remember the name of this hiking area, but it is great).
http://www.spokanecounty.org/bp/data/Documents/Trails.pdf
This link has trail info for Spokane.
Liberty lake is also a great hiking area. It abuts the national forest if I am not mistaken. You can hike for days there if you want, and you are still within 30 minutes of Spokane proper.
If you go the other direction, down by the river where it goes under the main bridges right as you are coming into the city of Spokane.
There are great river trails, with nice beaches right down on the white water. Devils punch bowl, etc. There is a camping ground, where you can park, then hike along the river on both sides. There is a suspension bridge to cross to the other side.