One bit of advice that I would offer is that if you are looking at home is the suburbs but will be commuting to the city, be sure to check out the traffic situation during rush hour. There are so many people that look at homes in the suburbs on weekends when traffic isn't bad. Then, when they finally move it, they are surprised at how bad rush hour can be. The suburb of Plainfield is a prime example. On the weekend, traffic isn't too bad on I55 but come Monday morning, it's backed up for miles and you're still 30-some miles from the city.
The western suburbs do have train service that will bring you right to Union Station. Areas like Westmont & Downers Grove have relatively low property taxes and good schools. They are older communities and are pretty much built out so they aren't needing referendums to build new schools like those further west (Plainfield, Oswego, Aurora...)
Park District programs can be difficult to get into in some communities (Naperville, Plainfield for example). Bolingbrook has one of the best Park Districts in the country. Bolingbrook is a little less expensive then the surround suburbs so many people will choose a home in Bolingbrook (because of the park district programs) that is located in the school district that they want. Currently, there are 5 different school districts all with-in the village border (203, 204, 365U, 202 and 68/99)
Be prepared for sticker shock. Home prices in this area can be much higher than other parts of the country but not as bad as it is out East. The average home price in most of the western suburbs is over $300,000. Places like Highland Park in the North Suburbs average over the 1/2 Million mark. Property taxes are based on the assessed value of the home.
Like others said, you will get a lot of advice but the best thing to do would be to talk to several realtors and see for yourself. Good luck with the move!