Have you contacted student housing? It will be difficult to find housing in this price range. It would be best to look closer to the date of arrival as well since rental properties move quickly. Please feel free to contact me if you need further assistance in your search.
I actually have an SAIC student moving here from New York who is in the same price range as you & would like to have a roommate or roommates, since there is very little available in that price zone. Also, short term rentals are very hard to come by & usually cost more. Contact me at 773-914-5309 or email@example.com. Barbara Biederman, City Point Realty