I am an independent Broker who lives and works in Rogers Park and I would be happy to assist you. Please feel free to contact me by email or phone. Link here: http://chicagosnorthcoast.blogspot.com/
That is a difficult price point even for Rogers Park. If you are able to get around neighborhood do look for for rent signs and call. Also many landlords are still requiring credit checks. As one colleague pointed out craigslst can be a source as well.
Best of luck