Pacific Science Center is cool, that, the MoPop, and the space needle are all within like a couple of blocks of each other. You can then take the monorail to the Westlake mall (original Nordstrom) and Pike's place is like 3 blocks away. From Pike's you can walk do the waterfront where there's the ferris wheel, the aquarium, and my favorite place to eat in Seattle Ivar's acres of clams. Ye Olde Curiosity Shoppe is there too, which is worth a visit just to see the mummies and stuff.
The Museum of Flight is phenomenal, but almost down to the airport and you pretty much would need either an uber or to get a car to get there.