You can get to Coney Island via the subway system, or at least within a few hundred feet.
I strongly recommend heading to e.g. the Grand Central Station information booth, in the middle of the great hall, and getting a subway system map. It will make navigating the city so much easier. The subway is extensive but not always the most intuitively obvious to decode.
Whether or not it's worth seeing is hard to say without knowing what you think is worth seeing. I personally would consider it a worthwhile trip, but then again I rather like amusement parks and rides, and they often tend to factor into my vacation plans.