Seattle actually does have a lot of dirt/gravel trails mixed in with city in parks. You have to know how to get to them, and depending on where you live you might have to drive or bike there if you want all of your runs to be trail.
I live about a mile north of UW and the commute to SLU is about 30 minutes most days during rush hour. If I leave before or after rush hour it's about 10-15 minutes. I like the area I live in because it's easy to get to some good running spots (Green Lake, the Burke, and Ravenna Park) and the local track where workouts are held.
If you're a competitive runner it's a really great place honestly. I ran a local road 5K last year (1287 finishers, no prize money) and in 18:51 I was 19th woman. I know this invites a lot of jokes about being really slow, blah blah blah, but back in Maryland that kind of depth at a local race was basically unheard of. CNW is awesome, it is basically my second family, and if I ever need to leave for work or school I will be very sad.
Outside of running, Seattle is a city of neighborhoods, which means that each neighborhood has its own unique atmosphere. The only real way to know where you'll fit in is to visit some of the neighborhoods.
Also, it is very bikeable. Hilly, but bikeable. I just learned how to ride a bicycle last year (like, at all, in a parking lot) and I don't feel scared riding around the roads here. Lots of bike lanes. Cars are really nice.
And it's safe as sh*t compared to most cities. I can go running at 5AM or 10PM and not feel nervous.