Gasworks park has amazing views of downtown Seattle and is next to a beautiful lake - Lake Union - and is where they filmed the paintball scene in 10 Things I Hate About You. :) If you're feeling adventurous and want to kayak on Lake Union, we highly recommend it! Kayak rentals are through Agua Verde Paddle Club.
Touristy market but still great. Clara's family goes to nice dinners here occasionally. See the gum wall! Catch a fish (if you ask nicely one of the fish vendors will throw a fish at you and you can try to catch it. It's a reasonably sized fish actually)! Buy weird collectables!
This glass museum + garden features work by Dale Chihuly and it is stunning. His work is inspired by the ocean, and you get to walk through and under blown glass eels and sea stars. It is right next to the Space Needle, so you can walk by that after viewing. The final room has a view of it - as you can see in this pic I took!