Although I didn't personally stay there, there were no rooms available when I Went, I would say check out the Best Western River North hotel. It is within walking distance of Navy Pier and the Magnificent Mile, close to the train/bus stations, has an indoor pool for the kids and FREE parking with reasonable rates. The cost to park is rediculous in Chicago!
There are two attraction cards for Chicago, the City Pass and Go Chicago Card, the website chicagotraveler.com has the breakdown on each of these cards so you know which would work best for your family. It also tells you when the free days are at the different museums, so it is a useful sight for planning your trip.
My kids are also 8 and 10 and they each enjoyed the Museum of Science and Industry a lot, the Field Museum a little and Shedd Aquarium not at all. The MOSI was very hands on, the Field Museum was not so much. The Field has a really cool Egyptian display and my son loved seeing Sue. We went to the Field Museum and Shedd on free days and it was SOOOOO crowded so that is part of the reason we didn't really enjoy the aquarium. We didn't pay extra to see the better displays and it was shoulder to shoulder crowds at both venues. Budget and Chicago don't go hand in hand, but with a little research and going in the off season you can have a good time that doesn't break the bank! Just remember to take some time to enjoy a walk along the lakeshore (it helped my husband and I to maintain our sanity during our trip!
) and have a great time!
Oh hey, I just saw that you are from KY and I am from southwestern IN. Since you will probably be taking I-65 through IN I would suggest that you spend some time exploring the Indiana Dunes. It was by far our favorite part of our trip to Chicago! We stayed at the new Best Western Portage Inn and Suites. It had a nice indoor pool, free breakfast and was close to the Indiana Dunes State Park and not too Far from the national park. Also, be sure to take plenty of change and dollar bills to pay the tolls!