Chicago is Museum Heaven.  I used to love going there at a kid.

Shedd Aquarium
Field Museum of Natural History and see Sue, the most intact T-Rex in the world
Museum of Science & Industry
Adler Planetarium

Navy Pier might be worth a stroll if the weather's nice, and the nearby Chicago Children's Museum could consume an entire afternoon and even wear out a certain granddaughter for an early bedtime!

I love Rob's suggestion of American Girl Place.

Finish with a trip to Whimsical Candy

There is so much to do. The museums are wonderful. The Field Museum of Natural History has a collection of dinosaurs that are sure to impress. The Shedd Aquarium was a favourite of our kids. The Museum of Science and Industry is also fantastic. Take her for deep dish pizza (Giordano's is our favourite). The hop on hop off bus tours are a good way to see the city. If she likes American Girl there is a shop right down town.

I would definitely take her to Lincoln Park Zoo. I take my nieces and nephews there at least twice a year and they never get tired of it. I would also recommend The Art Institute of Chicago. It is just a wonderful place for all ages. Go see the Thorne Rooms in the lower level. They are like mini dollhouses. I believe they also have an audio tour that is just for kids. And it is right next door to Millennium Park where you can visit the Bean. Have a great time!

Love the museums (Museum of Science and Industry), including the Shedd Aquarium, but if you're going on the weekend I would suggest going when they first open.  Navy Pier has lots of tourists but also lots of things to do, including the Chicago Children's Museum.  And the Lincoln Park Zoo is always fun.  With a 7 year granddaughter you'll probably have to pay a visit to the American Girl store - and eating there is always a hit with young girls. 

American Girl Place if it's still open.  

The Children's Museum in Oak Lawn by the Navy Pier

Rainforest Cafe

Museum of Science and Industry

Hi Evelyn-

Lots of great suggestions here, so instead of duplicating I will just add Maggie Daley Park. It's immediately east of Millenium Park and has a huge new playscape that just opened last week.

Also, if you head to Navy Pier (which is also the location of The Children's Museum) I would suggest taking public transportation as parking is pricy! I was recently there for 2 hours on a weekday and it was $22 to park. If you're not familiar with Chicago Public Transportation, the Google Maps app, allows you to put in your destination and then choose how you want to get there. If you choose the bus icon it will direct you on buses/trains.

Have a great time!

Field Museum of Natural History, Shedd Aquarium, The Art Institute of Chicago, Lincoln Park Zoo & Millennium Park and The Bean