Amazing. I live close to Mt. Si, Rattlesnake Ridge, Mailbox Peak and Crystal. I want to hike with some friends or go on a mountain run, just a half hour or so and I'm there. If not for all the rain this area would be heaven.
I agree with the above poster. The cascades are horrible. I don't know why anyone in their right mind would move there. It rains all the time, people are jerks, and the gays can get married. They even treat women as equals there. Crazy. I'm telling you don't move out there or you will regret it.
In other words, they suck more dick than the people who inhabit them.
Having lived and run in Seattle (near the Cascades), San Francisco (Marin Headlands), and Los Angeles (Santa Monica Mountains), I found most Cascades trails to be a little narrow and rocky for my running taste. You don't get many smooth double-track trails -- more like narrow single-track. Definitely invest in a pair of sturdy trail running shoes. Great views, though, and lot of open space.
The Cascades are really amazing! If you love to run and hike you will enjoy them.
One thing to keep in mind is that the snow can stick around for a long time. In most years it's likely that you can't do a hike above 5000ft without finding significant snow before the beginning of July. (Especially west of the crest.)
There are smaller mountains around Issaquah (Tiger Mtn) and North Bend (Mt Si) that are mostly snow free even in winter and offer great running. Although these locations are very popular.
I have two secrets to endure the perpetual grey skies and drizzle:
1: Solitude. When it's raining is a good time to enjoy the usually popular/crowded trails. While everyone is inside crying because of the weather, you have the outdoors to yourself.
2: Drive east! Particularly for hiking. Especially In the spring/summer months, if you drive far enough east (likely just east of the mtn passes) you will find sun most of the time. Eastern Washington is a desert.
The PCT is a great trail to run, since it's not too steep (suitable for stock) and well maintained.
The Teanaway is also a good place to run, it's farther east (sun), and there are several interconnecting grid-like trails. Gated or washed out forest service roads make good running trails.
The Carbon River Road at MRNP would make a good run since the road is damaged and will never be repaired. You can run the road to the campground then up the trail to the base of the Carbon Glacier, or take a side trail to something else interesting in the park.
The Iron Horse State Park Trail is awesome for speed work at "elevation" since it's an old railroad grade. Yes, 2500' is altitude training for those of us living at sea level.
I've always wanted to do a workout in Grand Park at MRNP. Park outside the park near Lake Eleanor, warm up run to Grand Park, then do the work out in the flat plateau (called a park) of Grand Park with amazing views of the volcano.
Don't forget about the Olympic Mountains.