I have to go to New York City to see attractions...help on what order I should go in?

Although most of those places are in Manhattan, I hope you will have several days to spend. Ellis island and Statue of Liberty require a ferry and will probably take up most of the day. You'll want to set aside a whole day for Coney Island too, because it's over an hour subway ride from Manhattan, and there is a lot to see there. Sagamore Hill is in Long Island, so you may have to give that one up, or devote yet another day for that too. You will need to take several trains (LIRR) and perhaps a car service in Oyster Bay. Other than that, allow yourself about an hour travel time between locations just to be safe, and plan to spend about an hour at each location. Good luck.