Statue of Liberty tickets are hard to get...and even with tickets you are in for a long wait just to go to the acutal islad, which is really a highly overrated trip, and a waste of time IMHO. It is far easier to see the Statue on a boat tour like the Circle Line boat tours. Even though you do not go to the actual island you are near enough to see the Statue and take photos.
The Circle Line departs from Pier 83 at 42nd Street & 12th ave on the Hudson River., and run from 75 min-3 hours ($24-34), April- Sept their ours are: 75 min tour: Daily: 11:00am; 1:00pm; 3:00pm . 2 hour tour: 11:30am; 3:30pm . 3hour tour: 10:00am; 12:30pm; 2:00pm; 4:30pm . I would recommend these tours (not really necessary to do the whole island--I have done it and it is a bit long).
Semi Circle Cruise- 1.5 hours, does lower Manhattan, you see the Statue of Liberty, etc.
Liberty Cruise: 1 hour: Like the Semi Circle cruise but only the left side of Lower Manhattan.
What is nice about these is you also get a feel for Lower Manhattan, Wall Street, Battery Park, and the area where the WTC is/was, without having to actually go down there. (Though it is a beautiful area, esp. batter Park).
