I would recommend Alliant Credit Union. They pay 0.65% on their Checking Account and 1.25% on their Savings Account. Only requirements for the Checking Account are receiving e-statements instead of by mailed statements and 1 electronic deposit per month. Only requirement for Savings Account is e-statements instead of mailed statements. They have a large network of ATM machines and offer $20 worth of ATM fees reimbursed per month if you need to use an ATM outside of their network. They do have a branch in Chicago at 11545 W. Touhy Avenue Chicago, IL 60666.
http://www.alliantcreditunion.org/