I still remember my first trip to Chicago as a kid, and the two things that stand out are the Sear's Tower and the amazing dollhouse at the Museum of Science and Industry. I've been hooked on museums ever since!
Are you familiar with the Association of Science and Technology Centers Passport Program? (www.astc.org) I just read about it on someone else's GoList the other day, and I am very excited. At first it doesn't sound like the most exciting thing in the world for kids, but if you buy a membership to one of the participating museums, you get into 280+ museums around the world FREE! It includes a large number of children's museums (unfortunately not the one in Indianapolis), discovery centers, space museums, aviation history museums, as well as the Field Museum and the Museum of Science and Industry. I'm not sure about your area, but several museums in Indiana have family memberships for $50. That would pay for itself right away if I visited the Field Museum and the Museum of Science and Industry.
To read more about it and search for participants:
www.astc.org/members/passlist_about.htm
I've never been to the Shedd Aquarium or the Adler Planetarium, so I can't give you any advice about that. I definitely think you ought to visit the American Girl Place! Great choice! I just stopped in briefly because I was with a friend who needed to go in there. I am a grown woman and I was hooked! Boy it was hard to leave that place without spending a fortune. Definitely an exercise in willpower!
I enjoyed the John Hancock tower. Your kids will probably like it as much as I liked the Sear's Tower when I was a kid. I haven't been to the observatory, but we celebrated a (grown-up) birthday in the restaurant at sunset and it is a wonderful memory!
Navy Pier is what it is. It is touristy and can be crowded, but there's also a festive hustle and bustle about it. The Ferris Wheel and the view of Lake Michigan is nice. Wear good walking shoes. We've gone early in the day and late in the evening so the sun hasn't been bad.
We took one of the boat tours that you can get from there and enjoyed it. Since you can walk along the river and see a lot of what you see on the river tours, I think I would have chosen a Lake Michigan tour instead. Here's a comparison chart of the boat tours. http://www.chicagotraveler.com/boat_tours.htm The boys might especially like the tall ship tour. http://www.tallshipwindy.com/ There's even a Pirate Dinner Cruise!
Someone might have already mentioned this, but definitely look into the free trolleys if you're going in the summer. (I think the one to Navy Pier runs all year, but the others don't.) They go past most of the popular sites and save little legs from too much walking.
Millennium Park is very cool. The kids should love the Cloud Gate Sculpture. Right across the street is a visitors' center. www.millenniumpark.org The trolley goes right by it.
If you want to have a picnic lunch, a few blocks away from the park is Spa Cafe. (spacafe.com) I really like the food. I'd eat there all the time if I lived closer to it. Don't tell the kids, but it's actually healthy too. Check the menu on the website. You know your kids and you'll know if that's the kind of food they like. (Note: They're only open M-F 7am to 4pm.)
The art museum is by Millennium Park, I believe, and it was ranked one of the best art museums for kids.
Farther north (and west, I think) is the ornate white Wrigley Building. It isn't really a destination in itself, but it's right by the river, and once you've been to that area you'll notice it in lots of movies and TV shows. One of my favorite movies is WHILE YOU WERE SLEEPING. They have hot dogs right by that bridge by the Wrigley Building, they walk along the river when he walks her home at night, and the fancy curved apartment building where Peter lives is right at the end of Navy Pier. I happened upon these spots since I was staying closeby, but that reminds me that the Chicago Greeters (which someone else mentioned) offer a film themed tour. www.chicagogreeter.com/Greeterdescript2.html
That's all I can think of for now. If I think of anything else I'll let you know! I hope you have a wonderful trip!