I think you are on the right track by renting before owning. It's always a good idea to talk to a mortgage professional to discuss how to increase your credit score. This is important to do now, as there are no quick fixes to increase your score. This process can take up to a year, depending on how much improvement is needed. Most lenders will not lend below 600 credit score.
As far as areas that will rent with those credit scores, I don't think that is area specific as much as it is the decision of the actual landlord. It really depends on why the credit score is so low. As a landlord myself, I would be more concerned about what's on the credit report more than just the credit score.
I have a listing in the river north area of Chicago. Feel free to call me to discuss or if you would like to schedule a viewing.
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