This may be out of your price range, but the Tower on Ryan Park has studios for $599 a month. More for larger apartments. It seems to have security and all that. There are several new places to rent downtown- just make sure there is security. Typically they have a doorman and all that.
Apartments for rent - ApartmentFinder.com They have a magazine you can order, too. They have virtual tours of some really cool downtown apartments. I think if I was in your situation, I would look into these downtown places even if it's just a studio. Downtown's really safe, actually- people just have to be aware and someone is usually around to help.
Wow, I looked and was surprised how expensive apartments are now.
Also look in the De Tonti Square Historic District which is just a few streets north of downtown. There are a lot of rentals there. We renovated a house there, and I can tell you it is very safe and quiet. Same with south of Govt. which is Church Street East Historic District. But don't go South past Canal Street. I don't mean to imply it's unsafe south of Canal but just giving you easy rule of thumb.
Oakleigh Historic District is about a mile from the ship area. Avoid the apartments, rent a house. Look just south of Government St. from Broad Street to S. Ann St. Don't go further south than Savannah Street. There are some areas north of Government opposite that area that are fine for what you need.
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