The Flatiron district, home of its namesake skyscraper and the jewel-like green space known as Madison Square Park, is a place of endless reinvention. Later this year, for example, Mario Batali's Eataly, an emporium of gourmet restaurants and food markets, is scheduled to open at 200 Fifth Avenue, and the owner of the iconic Flatiron Building plans to convert it into a luxury hotel. For a close look at this always-morphing area, take the N, R or W line to the 23rd Street subway stop. And come hungry. In another of its incarnations, the district is a restaurant destination. NOON The Flatiron Building, 175 Fifth Avenue, is just steps away from the 23rd Street station. Once known as the Fuller Building, after the family that built it, the Flatiron, which opened in 1902, is one of the city's first skyscrapers. But it has another notable trait: The building sits apart from others, enabling viewers to see it all by itself. ''It's the only skyscraper where you can take a picture, from streetscape to skyscape, with no interruptions,'' said Miriam Berman, author of ''Madison Square: The Park and Its Celebrated Landmarks.'' Admire it in its unique, splendid isolation. [ABSTRACT FROM PUBLISHER]