Guess you may already be away on your trip, but anyways at least for future reference I'll post a little since I'm familiar with MDW
is both good and bad for spotting. Its good because its smack in the middle of the city, and there are roads and sidewalks completely surrounding the airport. If you were in the mood for a workout you could theoretically walk around the perimiter of the airport (approx 4 miles). The bad part is that most of the perimiter fence has been replaced by "sound barriers" which you can't see through. There are some areas that are still chain-link fence, but not as much as it used to be. Many families stand along these fences with their kids to watch the planes and aren't bothered, but staying for an extended period taking pictures may bring some attention to you.
There are a few good places to park and spot...if you're hungry there is a White Castle at the corner of 63rd and Cicero right under the approach to 31C. Fanstastic views of landing aircraft when they are using this runway. There is also a Giordano's Pizza right across the street from the White Castle which has great food in addition to a good view. If you visit either of these places be sure to buy something, they hate people who loiter without making purchases.
Finally, some people have said the top level of the parking garage is good for picture taking, but haven't tried it myself yet.
Enjoy the airport, it has improved immensely with the opening of the new terminal last year!