There is incredible hiking in the Seattle area. If you're interested, ask Ben and I about some trails we recommend.
Sammamish State Park: lakeside beach and picnic area, some short walking/biking trails, in Issaquah
Kubota Gardens: Japanese Gardens in West Seattle area
Bellevue Botanical Garden: free botanical garden north of Issaquah
Washington Park Arboretum: massive arboretum in Capitol Hill area of Seattle
The beaches in Seattle are nice for walks and public fire pits, not so nice for swimming
Alki Beach: West Seattle
Golden Gardens Beach: Ballard
Museum of Pop Culture: downtown Seattle
Space Needle: downtown Seattle
Chihuly Glass Museum: downtown Seattle
Pike Place: downtown Seattle
Museum of History and Industry: Lake Union, Seattle
Museum of Flight: free first Thursdays, South Seattle
Woodland Park Zoo/Rose Garden: north Seattle
Gasworks Park + playground: Lake Union
Lake Sammamish Animal Sanctuary: Renton Highlands