Mountains & Beer
Snow Lake is a fantastic hike that's still only about an hour from Seattle. It's a moderate hike, so nice for out of towners that are in shape. Pack a lunch and bring it with you to enjoy by the lakeside.
I would stay at: Downtown Seattle
Anywhere in the standard downtown area is fine to stay in. It's very central to all neighborhoods. You can walk to Capitol Hill, Lower Queen Anne, South Lake Union, Belltown, Pioneers Square, and even SoDo. Not to mention that every bus passes through, and you're near Pike's Market.