I lived in Seattle for about 9 months (October-July) and there is way more to do than I expected. Of course, going up the Space Needle is a must-do. We did that just before sunset, took a couple of pictures when it was still daylight and then during the sunset and when it was dark. You can stay up there as long as you want and this is a way how to get loads of different pictures. I also visited the Aquarium and the zoo. Both are nice, but without children, not really necessary to visit. Besides, a trip to Pike Place Market is great. Do not only look at the shops on the ground floor where you enter. In the lower, you can find real fun shops that you won't expect. I especially liked the one with old photos for sale.
One of my favorites is Discovery Park. As I figured, it's not a place that you first think of when you think about Seattle, but it's beautiful. It's a huge park which you can enter from different sides. On the very end, there is a small lighthouse and a beautiful view over the (snowy) mountains. If you are lucky you can even see Mount Rainier. Btw: Mount Rainier itself is worth a visit. If you can choose, go on a sunny day, because it's a little disappointing when you cannot even see the mountain top.
Talking about views I definitely have to mention Kerry Park. In my opinion, it's not really a park, it's only a small green area with a sculpture and some benches. But it is definitely the place with the best view over Seattle...and again, if you are lucky, over Mount Rainier. Here you can find a picture of that beautiful
Another great part of Seattle is Alki Beach. On the way there (when starting in Seattle) you pass by a parking lot from where you can see the whole skyline of Seattle. And just a little bit further, you reach Alki Beach. Another nice beach in the Seattle area is called Golden Gardens with a playground for kids.
I hope I could help and everybody enjoys their time in Seattle as much as I did.