Choosing where to stay in New York City can feel like trying to solve a puzzle with a hundred different answers. Do you want to be close to Times Square? Would you rather have a quieter neighborhood to return to after a busy day? Is it worth spending more on a hotel if it means less time commuting? These are the questions I’d ask before booking anything. New York has hotels in just about every price range, but the neighborhood you choose can have a big impact on your experience. The good news is that you don’t have to spend…