I went to Ellis Island and Liberty Island. Now, I made the mistake of thinking that since summer had not started, that I would have no problem walking up, buying a ticket, and getting on the first ferry to the islands. Boy was I wrong. So, I recommend purchasing tickets ahead of time so you won't have to wait in the same line as the rest of us poor schmos who waited in line for a full hour before getting on a ferry. Reserving tickets is no more expensive. You just have to know what day and time you will be there to use your tickets.
I also went to see a play on Broadway. Instead of paying full price, check out http://www.tdf.org for discounted theater tickets. One of the ticket booths is on the South Street Seaport. There is another ticket office in Time Square but I recommend avoiding that booth along with the area at all costs. It's way too crowded. There will be a board with all of the shows that offer discounted tickets. There will also be people you can ask questions of and get descriptions on what the plays are about. Get there early, at least 30 minutes before the booth opens to try and ensure you get tickets to the show of your choice. See the website for more information.
Last, but not least, I went to New York to eat. I highly recommend checking out the food trucks in the city. Food trucks are not the same as the street food vendors. Food trucks are usually trendier foods with better ingredients (think braised beef tacos with pickled onions). But, since they are competing with the food vendors and nearby restaurants, their prices are very affordable. This is a great way to eat something tasty and keep your costs down. It's also a nice way to enjoy all of the public parks New York has to offer. Assuming the weather is good, you can sit outside and enjoy the view while eating delicious food. If you have a smartphone, look into downloading one of the many food truck apps that are available. Also, you can follow most of these food trucks on Twitter.