I live in Seattle now and have traveled around the state. Downtown and Capitol Hill are fun but way overhyped. I've gotten a better vibe from neighborhoods like Fremont and Wallingford.
Mountain hiking trails with lakes are great. Get all sweaty climbing up then swim in the lake to cool down after. I've done
Margaret Lake once and
Rattlesnake Ledge a few times now. They're fairly easy hikes to take visiting friends on.
Since you're southwest a bit more you should try and check out the Olympic National Park if you're into outdoors stuff. I haven't had a chance to get out there yet myself.