I second the choices of both Charleston and Providence.
15 years ago, when I first started traveling back and forth between New York and Providence for a consulting gig I was working, it was a culinary deadman's land. My how that has changed.
Charleston is unique because, until the recent departure of Johnson and Wales Culinary School for Charlotte, they were training a whole generation of chefs to cook serious food using local ingredients indigenous to the southeast coast. While fish and other seafood play a major role in the cuisine of that area, there is a real penchant among those chefs to cook local game also including, but not limited to local duck, local quail and dove, and local sweet corn, other summer vegetables and fruit.
Having mentioned the relocation of Johnson and Wales to Charlotte a couple of years ago, it certainly is ripe for undiscovered exploration as its first J&W class ventures out into the world of work in that former culinary wasteland. Charlotte has also developed a strong Central American community in the last ten years as it has needed labor for the unbridled building boom that has taken place there.
If you wish to explore that marketplace, I would strongly suggest making the acquaintance of Tricia Childress who is the restaurant critic for the local "Creative Loafing" weekly. She's very knowledable on both chow and fine dining.