I've done this a few times now so take my advice don't go from Battery Park! during peak season. You will be waiting on line for hours! Instead, jump on the PATH train over the NJ and then get the lightrail to Liberty Park. Spend some time exploring the park and then make your way down to take the tour from the bottom of the park. If you want to head back to New York after just go back over to Elis Island and then take the ferry back to NYC. You will get some epic views of the NYC skyline, save hours queuing and get to explore Liberty Park. Wins all round!