Mount Vernon comes to my mind first we stayed there about 7 years ago. Rent was affordable but the location has a few drawbacks. we felt a little out of it up there and hauling groceries from the car was a pain. In Orient Bay there are low cost rentals most are further from the beach and restaurants but if you have a car that wont be a big issue. We have been staying 2 to 3 months now that my wife retired and found that all places will reduce rates for longer stays. A place that fits you needs is the Shamrock Hotel first left after the guard shack. we toured it about 6 years ago and it was kind of unique and very affordable then.