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OP you should look at Wilmington NC, Charleston SC, and you should also go ahead and look at Savannah GA. All three are cool cities, with rent prices at your range and even under, with the beach being like 15 minutes drive from downtown.
You also might want to consider the smaller towns of coastal Connecticut, east of New Haven. Those are places like Stonington, Groton, New London, Mystic, and the like. This is affordable, working- to middle-class Connecticut -- not the uber-affluent suburbs of New York City. Many beach options nearby, basic New England four season weather, and two hours (at most) to NYC, Providence, New Haven, Hartford, or Boston for big city adventure.