In my opinion.....since you are moving to the Chicago area, stay away from First American Bank, they will nickel and dime you to death with fees.
If you are moving to the burbs, check out Chase/Bank One. I recently moved my checking account from First American Bank to Chase/Bank One. My primary motivation for selecting Bank One was simply that they have the most Branches/ATM locations in the Chicago Suburbs, plus they have an ATM in every Walgreens, and most Dominick's stores. Also, the Bank One website is one of the best I have ever worked with (and I have worked with many), especially if you use Quicken or Money to track your accounts (as I do).
If you are going to live in the City, then Bank One may not be the best choice unless you live downtown, otherwise not too many branches. If you prefer banking with a smaller bank and are in the NorthWest burbs, check out
American Chartered Bank it is locally owned and operated, my wife used to work there and we had a checking and savings account with them for a while and we had no complaints.