Whoot whoot +1 for S. Snoco, my hood. I'm in Edmonds. Very good schools, very safe. Nice place to raise a family and lots of amenities like parks, beach, ferryrides, etc. $300K is doable, particularly for a condo or small home. Also direct, if limited, train service to king street station in Seattle.
Edit: Something else just occurred to me, since you are talking about biking to Lake Union. Not sure if you've looked at this
http://www.seattle.gov/transportation/docs/2012BikeMap.pdfbut the Interurban Trail has good connection from Shoreline (goes all the way to Everett, actually, but that's pretty far to bike commute) in N. King County to Seattle including Lake Union, though in city the trail goes on road I think.
Shoreline, as an example, has good schools, is a nice family friendly area with a wide range of neighborhoods and price points, including very affluent and more value-centered, but except for a few pockets along Hywy 99 most of Shoreline is really nice. It might be worth it, since a lot of family friendly neighborhoods are north of the city, to follow the path of the Interurban and see what looks good to you that would still be bike-doable.
Good luck!