The newly paved grounds of Union Square, bordered by brightly lit department stores and hotels, may not at first seem like an inviting place to hang out. But perch awhile on a skinny bench or grab a coveted seat at the café in the square, and you’ll discover some of the best people-watching in the city.For in one day, you’ll see theater-goers debate the merits of the latest David Mamet productions, Nob Hill society dames in dark glasses duck into Maiden Lane spas for facials, and giddy teens wear out their parents while shopping for prom dresses.But the real reason to come to Union Square is to shop. The square is home to six major department stores: Macy’s, Bloomingdales, Barney’s, Nordstrom, Saks Fifth Avenue, and Neiman Marcus. Boutique shoppers will find plenty of spots to browse the latest designer fashion. High-end emporiums surround the square, including Louis Vuitton, Gucci, Bottega Veneta, Dolce & Gabbana, Burberry, Prada, and Giorgio Armani.