Don’t encourage Himalayan blackberry in your yard unless you are prepared to deal with the consequences. It takes some serious goats to gnaw those things to the ground, and they will just come back. Instead, go to one of Seattle’s many blackberry patches for pretty much all-you-can-pick. Vacant lots, undeveloped hillsides, and parts of certain parks (Carkeek being my favorite) are havens for the blackberry.
There is also native blackberry, and black raspberry, which are unfortunately somewhat hard to find in the city in my experience!