Warren G. Magnuson Park in Seattle is a former Naval facility that now offers not only beautiful green space, views of Mount Rainer, Lake Washington and the Cascades, community gardens and great places for kite flying (35-foot Kite Hill) but also has a cool playground for kids. It's especially great if your kids like to climb. The Junior League of Seattle Playground has more climbing structures than any other play space in Seattle. Climbers of all skill levels are welcome, including toddlers who can try scaling the toddler-scaled structure.
Also, for those out there with fur-babies, Magnuson Park is a popular spot for off-leash dog romping.