Seattle's public zoo, the Woodland Park Zoo is located just south and west of Greenlake, at the intersection of Fremont, Ballard, and Greenlake.
While it's not the largest zoo in the US, the Woodland Park Zoo has done a good job of providing a habitat for a wide variety of animals in an urban, pacific northwest setting. When we last visited, the giraffes and penguins both seemed to be out and about despite the cool-ish weather. The hippos seemed pretty content to just lay on the ground, though when we went by the second time, one had mysteriously slid into the water...