Athena Calderone doesn't consider herself a design purist: "If you love some Georgian sideboard and you also love this supermodernist piece, just know that it can all work together," she says. In fact, pairings that challenge the beholder are the cornerstone of her lifestyle blog, Eye-swoon, where she posts fashion editorials, cooking tutorials with designers, and photos of interiors that catch her eye. "When things feel a little bit off to other people, that's the truest testament of your style." To that end, Calderone's two New York living spaces-a penthouse in DUMBO, Brooklyn, and a beach house in Amagansett, both of which she shares with her music-producer husband, Victor, and their 11-year-old son, Jivan-are filled with modern pieces from Danish architect Ib Kofod-Larsen, plush Dunbar sofas, and mix-and-match chairs unearthed…