Pike's Place Market is world famous for a reason. You can grab a coffee from the original Starbucks (or walk around the corner to one of the many Starbucks locations and beat the line). Stop by Uli's Sausage for lunch and don't forget to stop by the Pike's Place Fish Market to watch the flying fishmongers.
Every picture you have ever seen of the Seattle skyline is taken from Kerry Park. Nestled in the beautiful Queen Anne neighborhood. Parking can be a bit of a problem but it is a fun place to walk around and look at the million plus dollar homes in the area. While you are in the neighborhood stop by The Five Spot, one of the best breakfast paces in the city.
Outside of the downtown area is the Fremont neighborhood known as the more artsy side of the city which is filled with funky shops, restaurants, coffee shops, and home to the famous Troll Under the Bridge. The Fremont Troll is an art installation under the Aurora Bridge made from steel, wires, two tons of concrete and complete with a full size VW bug.