The biggest question is are you going to rent or purchase a home. Secondly, how much money do you want to spend on a home.
Third, how much money and time do you want to spend on the commute from wherever you choose to live and the downtown area of Chicago.
From there you can begin to look at neighborhoods and home sizes.
Check out the metra lines website to see how much the current commuter fares are.
Also check out the CTA website to see what "L" trains serve these areas as well.
The CTA, for example, serves Oak Park, as mentioned in one of the responses, and some of the North Shore suburbs...
A big determinant of where you move would be schools I imagine, as well as other people you know and/or family...and ethnicities. Some places are more diverse than others, and some places are less diverse.
Typically, living close to the lake is more expensive.
And, the lake does moderate weather considerably.
Typically if you live within one mile of the lake, summer temperatures can be moderated by the cooler lake breezes... at times a lot, on the order of 20 degrees or so, but not if there is a strong western or southern wind. The reverse can hold true in the winter, when temperatures can be warmer near the lake, again depending on wind. And finally, the lake front can also have more snow and rain than other parts of the area.
Finally,expressway commutes can be beastly and time consuming. Chicago is one of the worst commute time cities in the country. If you're commuting a distance of 15 miles from a suburb to the city core, figure on spending an hour or so. and if you go further out, figure on more time. plus city parking rates are outrageous, and the city is in the process of selling it's parking meters and garages to independent companies so the costs will only increase.
Also eating lunch and snacks in the loop is really expensive, fast food lunches will cost between $5 and $10 and aren't all that healthy either. Starbucks tall coffees are $1.65 and up, so the little treat amenities can start to add up.
Finally, gasoline in the Chicago area is one of the highest in the nation, regular is currently going for $3.80 plus in the suburbs and is at $4.00 and above in the city.
Of course on the plus side we have the lake which pretty much assures a plentiful water supply, at least for now. And being in the center of the country does allow for air travel to be more convenient, with more connections and more direct flights from two airports.
If you like getting to nature, then also figure spending at least an hour getting away from the city.
Take a look at Google Maps and you will see that Chicago and the surrounding areas are humongous.
Finally, a bit of advice about suburbs. Oak Park is sort of landlocked between a poorer section of Chicago and other suburbs.
For better or worse, the history of Chicago is that the more "upscale" suburbs have been located along the north lakeshore, and to some degree have spread out a bit west of the lake as well.
Small towns that used to be removed from the city have become part of the exurbia and there are actually people who commute 50 plus miles each day one way. Commute times, one way, are in the two hour range. And these small towns now have residents that commute to other small towns, sometimes at distances of 50 plus miles also, so at rush hour you have people going in all directions simultaneously.
Rush hour begins at 5:30 or 6 AM and lasts through 9:30 to 10AM, and then begins in earnest at 3:30 PM and lasts through 7PM or later...
If you like driving, the best time is early Sunday morning, when the Freeways are, well, actually free.
Finally, while Chicago has museums, they too have become expensive (figure on spending at least $100 for a family of 4) and theatre (it's possible to get tickets for $20 a seat, but unlikely), movies are now about $10 a ticket.
Choose where you live not for the glitz, but for the home feel that you prefer, and figure in the costs of getting around, and while we're on energy, electricity and natural gas need to be considered as well. Older homes are heating hogs in the winter and it's easy to spend $1500 to $2000 or more heating a 1800 square foot home.
Welcome to the Chicago!