You can’t throw a mustard-covered pretzel in New York City without hitting a hotel. There are about 700 of them in the city, but only a few are truly luxurious. Designer details, out-of-the-box amenities, Michelin-starred chefs, sumptuous suites, tony locations, and highly personalized service are all de rigueur. While many of N.Y.C.’s best inns are century-old institutions, very prominent newcomers are testing the old standbys’ ability to stay fresh. (In fact, many of the city’s legacy hotels have undergone full-scale renovations, with billions being pumped into the Waldorf Astoria alone.) “I think it was long overdue to keep up with other places around the world who have reputations as being incredible hotel cities, such as London and Paris,” Josh Alexander, a luxury travel advisor with ProTravel International, a Virtuoso agency, told Robb Report. “New York City was falling behind.” In short: It’s a race to up the ante that has resulted in “six, even seven star hotels,”..