I think the Seattle metroplex (though not Seattle proper) may be better suited than Eugene. I live less than a mile (as the crow flies) from the Puget Sound but can see snowy peaks not too far off.
The outlying areas (Kirkland, Bothell, Everett, Marysville, and more)—are pretty close, and if you catch the traffic flow just right, you can get to downtown Seattle in 15 minutes or so, or to the center of those communities (or at least somewhere decently cool) far quicker. There are some places around here where they are so relaxed that a non-native would check the natives for a pulse.
I happen to live in a fairly quiet suburban neighborhood with woods nearby yet only minutes from a few different varieties of city life. A good place for a family, I would think.
The only downside really is price; the state and county sales tax are a combined 9.5%, and $800 for a 2-bedroom apartment is about normal. Being from New Hampshire, I am used to 0% sales tax. As for the rents, they are about the same as NH, but I hear from people in other parts of the country that $800/month is expensive :/
At least they two states have one thing in common; no state income tax :)
BTW, Seattle is considerably different from the rest of WA state, so don’t judge the state until you get up North, and for the love of Bob, don’t go East! There is nothing of interest there, and not much that isn’t interesting either. High desert with occasional gatherings of rednecks.