I'd suggest checking out West Seattle and Georgetown. Both areas can be a bit more affordable than some other districts in Seattle. I've not lived in Seattle, but I have friends and family who have lived in both areas.
Granted, Georgetown is (used to be?) more of an impoverished area and, as a byproduct of the culture of classim, has/had a high crime rate, lots of drug use/distribution, etc. Also, there are also a lot of reasonable rent prices, some really fantastic and affordable restaurants, awesome social justice projects, vibrant places of worship, etc.
Not sure about school systems.
West Seattle is a short drive from Seattle city center and looks across the Bay at the skyline. It is becoming less affordable, but you might still be able to find a cheap rent. My girlfriend who grew up there says it feels like a small town, lot's of old ties and connections and strong sense of pride and community. I guess it's an old working class neighborhood, pretty safe, decent public transportation routes, really cute shops and cafes, lovely parks, a lot of foot traffic and smiling families, etc.
There's a lot to do over here! Good that you love the water! Check out Point defiance Zoo in Tacoma (and actually, maybe living in Tacoma would suit you...some neighborhoods are not for the faint of heart and others are down right dangerous...also some are just gorgeous and there are so many fun museums and things to do around there), SAM, the aquarium in Seattle, Pike Place Market, take the ferry over to Bainbridge Island, come down to Olympia for Parade of the Species and the Hands on Children's Museum, go over to Hood Canal (try some of our Oysters, we have the best!), LOT'S of hiking - heck, we have some of the most beautiful forests in the world, and if you need a break from the clouds and drizzle (yes, it really is as bad as you've heard), head over to E. Washington for a few days. Port Townsend! You've got to go there! It's quaint!
I'll add more if I can think of some! Happy move and welcome to the area!
