You wont find anything in Seattle that meets your criteria. Prices drop going north and south for the city (and King County), but both are largely quite crime ridden as well. You can see breakdowns at:www.bestplace.netNorth: Shoreline, Lynnwood, Edmonds, Everett, Bothell.South: Renton, Kent, Auburn, Federal Way.
It is usually a LOT more expensive in King county (the county where seattle is) and renton is pretty expensive so i doubt you can find something that cheap. You can try rent.com or craigslist. I live in puyallup which is safe but you would have to search for an apartment that cheap and i m not even in King county. Tacoma has cheap apartments but a lot of the cheap areas arent that safe. Keep in mind that even the unsafe areas arent THAT bad..i mean you arent going to get shot. Seattle area is pretty expensive though so i m not sure how easy it will be to find something good less than an hour away at that price :-/
You might also want to look north in the Lynnwood area. You can probably find an apartment in your price range and it s a pretty quick and easy commute to Seattle by bus.
Housing prices in the Seattle area are rather expensive because historically commuting has been a nightmare. This may be changing with the advent of light rail and increased bus service, but due to the geography of the city there just isn t a lot more room to pave over for more freeways. This lack of convenient and cheap commuting means everyone wants to live near their workplace, and most people either work downtown in Seattle, Bellevue, or Redmond.If you truly don t care about access to Seattle itself, you might want to check out bedroom communities on either the Penninsula or one of the Islands in Puget Sound. Kitsap County (encompassing Port Orchard, Bremmerton, and Silverdale) has generally cheap rents and is accessible to Seattle via our ferry system.