Other fun things to do in Seattle (I am from there)
Argosy cruises does a fun harbor cruise during the day (right by the aquarium)- it's pretty informative and you can get great pics on it (they also have a bar on board). They also do more fancy dinner cruises for those in the area for a cpl days.
The Seattle Center does have some interesting things- check out their event calendar here:
http://www.seattlecenter.com/events/ - the children's museum in located in the center house there and while best for ages 8 and under I would say, is very fun for little ones.
The Experience Music Project (EMP)/Science Fiction museum is also on site there (at the Center) and fairly entertining (though pricey)
Also at the Center, is the Pacific Science Center. Often there are traveling exhibits here (recently the Harry Potter exhibit, then the Star Wars one). Very fun
The zoo (mentioned in a PP) is really fun, and Greenlake (a 2.8 mile loop) is a nice stroll with lots of restaurants and a playground. The lake is very close to the zoo (so if you are headed there then check it out). Both though are not in the downtown area.
A PP mentioned the everett area- if you head that way the childrens museum there is really fun, as is Forest Park (a great park with multiple playgrounds, a petting farm, and a water playground/splash park).
For those wanting to take a day trip out of the downtown area (you would def need a car, its 30 min out of downtown)- I would recommened Snoqualmie..they have an amazing waterfall located at Salish Lodge (which has 2 great restaurants and a spa onsite), as well as a cute strip in town with other dining options, cute quaint shops, a bowling alley, coffee shops, etc. The drive from downtown to Snoqualmie will take you completely out of the city and into a feeling of being in the true northwest (and it's a short drive!).
One thing I would HIGHLY suggest is getting a local entertainment book for here. Every school year we take orders (and you can get them online) and I know they run through the following November (so a little more than a school year, not a calander year, if that makes sense). Nearly every attraction people have mentioned is in there- usually a buy one get one free entrance. Some of those attractions are at least $10-$15 each and an Ent. book is only $25. We get two a year usually and if helps our family of 4 SO much. They have great downtown dining coupons, tourist attractions, etc.
For a good all inclusive site to reference (and it sorts things to do by neighborhood which is helpful) visit
http://www.cityofseattle.net/visiting/