If you want an indoor pool for kids, one of the best hotels in the area is the Sheraton 4 Points. The heated pool is in a sunroom enclosure on the roof. It is next-door to Neiman-Marcus at the rear of the Shops at Northbridge, which is the mall that contains the
Lego store. The location is very convenient to transport down to the Museum Campus and to Navy Pier. The Chicago Children's Museum at Navy Pier is not to be missed for that age group. (I know someone else said it skewed young, but that hasn't been our experience. Younger school-age kids tend to like the various building experiences in it, such as the foam airplane room, the water room, and the climbing ship, which doesn't allow preschoolers on unless they are freaky tall. Even my 12 yo still likes trying to build a fountain without getting drenched in the water room.)
The "Museum Campus" is the city's name for the complex that contains Shedd Aquarium, The Field Museum and the Adler Planetarium -- and also Soldier Field. The #130 bus serves the Museum Campus, as does the #146. The #10 is the express bus to the Museum of Science and Industry, which is down in Hyde Park. The Campus is just south of Grant Park on the Lakeshore, which puts it more or less even with the South end of the Loop. I honestly would not recommend staying down that way with kids, as except for the theaters and the theatre restaurants, the businesses in the Loop largely shut down after 6 pm. There is a lot more tourist action on the street up in the Mag Mile, so it's more pleasant to walk around up there.
Just so you know, the lines on weekend mornings to get into Shedd can be UNREAL. In summer it can take 3 hours to get through the line on Saturday morning. We tend to avoid Shedd unless we can go on a weekday, because on weekends it is often too crowded to be able to see any of the exhibits for more than a few seconds. It is also VERY dark inside, and it's quite easy to lose track of a child when the crowds are thick -- I recommend very bright clothing.
FWIW,
THE indoor hotel pool in Chicago is at the InterContinental. It's on the 14th floor, is Jr. Olympic-sized and done up like a Roman temple -- it looks like a set from an Esther Williams movie. It was quite the engineering marvel when it was built in 1929. However, it tends to be full of serious lap swimmers who are not too patient with kids just splashing around.