Going to the Shedd, you can park at Soldier Field, it is underground parking. The price varies, but I would count on it being $20-$25, and if you show up and it is less you can be pleasantly surprised. Sometimes they have a early bird rate if you get in before a certain time.
Just my suggestion on the Shedd. I took my kids there last year (they were 2&4 and my son was just a baby), and since there isn't a lot of interaction, my kids found it boring, it is pretty dark in there exhibits and if you want to see anything except the main viewing area such as the dolphins, there is an extra charge.
I personally love the shedd aquarium, but my kids are more active and want to touch everything, so the Museum of Science and Industries, is our choice for our hands on kids.
Whatever you choose, I know you will have a great time down by the lake. Dress warm, and bring your own snacks.