The Space Needle is probably what everyone first thinks of when they think of Seattle. The surrounding area has some interesting things too. I've made sections of the map clickable.
If you want to visit a bunch of places you can get the City Pass, which can be a cheaper option.
The Space Needle is not incredibly interesting to us. It's not even close to being the tallest structure in the city and the tickets are usually pretty expensive. Pacific Science Center is fun and they play regular IMAX movies in addition to the educational ones. The Experience Music Project shares space with the Science Fiction Musuem. The building is very unique.
Pike Place Market
Pike Place Market is another well-known spot in Seattle.
Pike Place Market has a bit of a farmer's market, the first Starbucks store, and that place where they throw fish at you. And it's right on the shore so there's a nice view. The cruise ships pull into harbor right around this area, as well as the ferries. Also really close is the Seattle Aquarium. The City Pass has admission to the aquarium.
One activity we did that was really fun was kayaking. You can get a view of the house boats (like from Sleepless in Seattle) and go through the Ballard locks. It's just fun to take a kayak into the locks. Plus a lot of the crab fishing ships from Deadliest Catch dock in Seattle. With a kayak you can paddle right up next to them.
Seattle is divided into a few neighborhoods. Pike Place Market is in the middle of the waterfront. The retail core obviously has all kinds of shopping. Pioneer Square has a few old buildings and is nice to walk around. For restaurants, Belltown and Capitol Hill are the best places. They have all kinds of stuff. A few microbreweries and some pretty quirky stuff.
Seattle is also home to Boeing. You can go for a Boeing factory tour and see them building the planes. It's a cool tour. The building where they assemble the planes is large enough to have its own weather inside. Also close is the air and space museum which is a pretty good tour too.
Seattle is actually built on top of an older city. The story about how it got like that is pretty interesting. We took my parents on this tour and liked it. However, it seems to completely depend on the tour guide and can be hit or miss. They take you through some of the preserved parts of the older city. There isn't anything really worth taking pictures of though.