If you have the time, take the ferry from Downtown Seattle to Bainbridge Island! This is the best way to view the city! The ride is short, and there are cute shops and restaurants on the island once you land.
The MoPop (formally the EMP) is our Museum of Pop Culture. All the Seattle-y music memorabilia your heart desires, with other seasonal exhibits. Plus, it looks mega weird, and it's right below the Space Needle (also pretty cool).
Linda's is our favorite dive. If you want decent breakfast/bar food, stiff drinks, grungy music, and questionable staff, we recommend Linda's. This was the last place Kurt Cobain was seen alive, so it doesn't get much more Seattle than that.
Easy Street Records is our favorite place to get diner-style breakfast in West Seattle! (And it's the cheapest). It's actually a record store, so you can browse before and after. Hope you like Pearl Jam.
Discovery Park has great views of the San Juan Islands once you take a short hike through the grounds. The weather will be great for this type of activity.
West Seattle (Best Seattle) is our neighborhood! There are plenty of things to do in WS including Alki Beach (bars, restaurants, bike rentals, views of the islands and the city), or California Ave/Junction (main street, bars, good food and thrift shops). Doll Parts Collective is our favorite thrift store. New Luck Toy is our favorite Asian restaurant/bar.