When I visited San Francisco a few years ago I tried to visit Alcatraz Island without buying tickets in advance and was told that that was pretty much impossible on account of the fact that they generally sell out of tickets days before the actual trip.
Places like Ellis Island don't appear to sell tickets online, making early sell outs impossible, but the Intrepid Sea, Air & Space Museum however does sell tickets online: http://www.intrepidmuseum.org/Plan-Your-Visit/Ticket-Information.aspx
My question is... should I buy in advance or is there a good chance that I'd be able to buy the day I wanted to see it?