as Ron said, take the #6 to the last stop and then take a bus. The bus runs fairly frequently. Once on City Island, the bus goes the whole distance of the island so you can get off (or on) at many spots. But, Jeremy, City Island isn't what it used to be. IMO, it's not nearly as interesting or funky as it used to be. Basically, it has become gentrified. Although not relevant to Kate's question, a transient sailor if anchoring will have a hard time finding a place to leave the dinghy. I was able to do so short-term at a yacht club but wouldn't have been able to leave the dinghy there and go into the City without paying for a mooring (fairly expensive, if I recall correctly). If you are spending any time on the boat, you don't want to be in - or across from - the City on the Hudson. In addition to the current, there can be wicked wakes caused by the big ship traffic. New York Harbor itself isn't really good for small boats, but it's nice on the LIS (City Island) side.
Jerry