Lots of good advice already so I'll chime in with some under the radar suggestions. Before I had kids, I used to go to Pioneer Square and walk around. I could spend literally the entire day just at the Elliott Bay Book Company, and at Everyday Music. The two stores are located across the street from one another. Very short drive (straight east) from Pike St Market.
Another nice place I liked hanging out at is Fremont. Lots of great restaurants and shops plus dozens of outdoor art installations to check out, including the famous Fremont Troll. Theo Chocolate is probably the most popular chocolatier in Seattle and their shop in Fremont offers factory tours with samples of all their different varieties of chocolates.
The Chittenden Locks in Ballard is a nice place to hang out on a nice day. The salmon run there is very impressive to see, although optimum viewing time is late summer.
Volunteer Park in Capitol Hill is another nice place to hang out. You can climb to the top of the water tower there and get some some nice views of Seattle.
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