My friend Deb lives in Seattle and we try to together every few weeks to catch up. The last couple of times we've seen each other we have met up a Seattle park so that we can get some exercise, fresh air, and walk her dog. I think it's great because Deb seems to know a lot about the different parks in Seattle (she does live there after all), so it's nice to go with her and have my own tour guide.
Discovery Park is pretty famous in Seattle, as it is the largest park the city has to offer. Once you walk away from the parking lot the trees surround you an you feel like you're in Mt. Rainier National Park, rather than the middle of a city. We hiked through forests, meadows, and along the beach. While we were sitting on the beach we spotted a bald eagle that had caught a fish and was eating it. I was able to get pretty close (and also got a close up of some interesting barnacles and what-have you) to get some pictures, without disturbing the giant bird. We also visited Lincoln Park one day which is in West Seattle. This park, while large, is not quite as big as Discovery Park. But I loved the beach access. People in this state love walking on the beaches when the tides are low. I think they like exploring the rocky shores and the starfish, barnacles, and urchins that live among them.