Jenny, there is a big thread in the main forum with stuff to do in Seattle. I can give you my suggestions, but you might want to dig up the big thread--it is way more comprehensive than anything I can post!
My kids LOVE the Aquarium. It is right on the waterfront. The new ferris wheel (Seattle's Great Wheel) is next door and also on the waterfront. These both are within walking distance of Pike Place Market--there is a staircase out the backside of the Market that makes the walk a lot shorter. Your four year old also might like seeing the (nasty!) gum wall that is underneath the Market. It is quite a draw for tourists!
If you walk farther along the waterfront, there is an indoor carousel that my kiddos love and then a bit farther along there is Ivars--which is a Seattle institution. It is a seafood restaurant (fish n chips) and it has covered and uncovered seating outside or there is a fancier restaurant inside. The street front restaurant is classic Ivars though.
The whole sidewalk between Ivars and the Aquarium is really wide and perfect for kids and families to wander along. Lots of shops to duck into. Ye Olde Curiousity Shop is crowded but fun--the back wall of the shop has display cases with artifacts like shrunken heads and stuff like that.
In the Pioneer Square area you could do the Underground Tour. I love it, but I haven't taken my kids (ages 8 and 6) because the air is a bit stale and I know my 6 year old would complain about some of the smells.
There is the "Ride the Ducks" tour that a lot of tourists do. Personally I can't stand it, but I know a lot of people like it. The Space Needle and the Pacific Science Center (with the King Tut exhibit) are at the Seattle Center.
If you are staying at Pike Place, you are right in the heart of things--walking distance to lots of stuff!
