Yea right good luck. Your best bet is to room mate for that little. Be leery of whom you room mate with as you might be getting more than you can chew. Redfin.com is a great too to use for apartment/house hunting. If your seeking room rentals you'll need craig's list (total gamble), nextdoor and other social media places. You're literally placing your self with a gamble in these situations. It could be good, bad or terrible. For one month you're not going to find much. Your best bet is to couch surf with someone if you have family/friends in the area. Rentals are one yr contracts. Yoru best bet is an airbnbs. Though that can be pricy.

Have you considered an extended stay hotel or homeless hotels. They're designed for impoverished individuals that need some where temporary to stay that don't have much money. You must meet certain criteria to qualify for them. Your room mates however won't be of the best clientele but that might be your best option. You have to apply now for them as the wait list is a bit long.