The most important question here: Shaken or stirred? Oliver's, in the Mayflower Park Hotel, is famous for its martinis. In fact, having a cocktail here is like having afternoon tea in some other parts of the world. Wing chairs, low tables, and lots of natural light make it easy to relax after a hectic day. The likes of Frank Sinatra or Billie Holiday may be playing in the background; expect an unfussy crowd of regulars, hotel guests, and older Manhattan-sippers who appreciate old-school elegance.