I always go up to Columbus Circle first thing and grab a Fun Pass for the Subway/Bus system. That gives me total freedom to roam the city at will. At night, however, my favorite thing is to just walk. We stay at 56th and 7th so it is a great walk to the Park, theater, restaurants, shopping, whatever.
Oh you are so lucky to be going to NYC for the first time. What a wonderful memory it will be for you.