Your budget will need an adjustment! I have only found 3 units in your price range in areas that are not too far from the loop, where I myself would feel comfortable living alone. These did not include utilities! You will need more money or perhaps a 3rd room mate. I will be happy to help you. Please fell free to call or email.
Fresh Horizon Realty
We cant comment on what is safe, but you may want to check out what is in your price range. That will vastly limit your area.
Also, get a good leasing agent to help. Its free to you!