Hi and welcome to living in the US. Chicago is a bit overwhelming, as there are so many choices. We ended up living in Hawthorn Woods, in a country club environment. We chose HW because of the gated community, the quietness and the closeness to transit. Our house is for sale, BTW, if you would like to check out the community - Protected content .
First, you do NOT want to drive to work every day, if you can avoid it. If you near downtown, in Cook County, you have the CTA to access downtown. Further out, like in HW or Naperville, you have the eleven Metra lines. The best way to see how the commute would be is to use google maps and the transit option. It won't let you figure the time including driving to the Metra Station. To do that there is an website called goroo.com, put up by the Regional Transportation Agency.
The first thing to realize for Naperville, is that parking is limited at the train stations to get downtown. There are plenty of trains, but the trains to Naperville get really crowded. HW is close (within 3 miles) of the Mundelein station, where parking is available and inexpensive. Metra train passes can be purchased in monthly, 10-pass and daily. Your employer may subsidize the transit in return for a tax break. It ended up being a easier commute for me to downtown Protected content to train station Protected content downtown) vs going to the Naperville station Protected content to station Protected content downtown). The Naperville trains are also more popular, so seating can be an issue. I lived in temporary housing in Naperville, so I speak from experience.
There are no issues signing up for good schools. There lots of public and private options in the Chicago area. The downtown areas (Cook county) actually have you interview - and the Chicago Public Schools are frequently on strike.
There are lots of things to do and see that you and your family would enjoy. We enjoyed doing things in the local area, Milwaukee, WI, Lake Geneva, WI and downtown Chicago.
My wife enjoyed going to the Harley Museum, and she is not a motorcycle babe. We also did St. Patricks day downtown (once) riding the water taxi to Michigan Ave to be in the green river. Your girls would enjoy the Museum of Science and Industry, the Aquarium, and the multitudes of art museums. Annually, there are architectural tours of dozens of buildings downtown, which everybody enjoys. It's called Open House Chicago - Protected content for details.
Enjoy! PM if you have specifica questions.