Stylish because of what it is not...

Joe Allen is my favorite restaurant in Miami. It has been open since February 1998 but it feels like it has been around forever, which is a good thing for a restaurant, especially one so off-the-beaten path. There are other locations in London and Paris and the original in New York which opened in 1965.
It is the perfect restaurant because of the things it's not. No "themey" decor or towering wall of liquor bottles behind the bar. No small plates or fusion food. No twenty-minute introduction by the server. The menu is loaded with things you actually want to eat (especially the deserts) and service is understated and professional.
Joe Allen recently opened another place in Manhattan called Bar Centrale which serves bar food, but with the volume turned up (grilled fontina and bacon sandwich; quesadillas stuffed with lobster). I predict that one will be around forever, too.