BE ADVISED: if you'd like a closer look, the Staten Island Ferry (which is FREE, do NOT let anyone try to convince you that it isn't) sails right past it. There are also (paid) tour boats that get a bit closer, but in Milaci's opinion, you might as well just take the Staten Island Ferry.
The best bookstore in the world. Seriously.
SPECIFICALLY this location (in Union Square). This Barnes and Noble has FIVE floors and a cafe. Another contender for best bookstore.
If you love Italian food, this is the place to be. It's a labyrinth of Italian restaurants, markets, and gift shops. The gelato here is DIVINE.
For those of you who'd like to see a Broadway play, there are two major ways to massively reduce the cost of your tickets: obtaining RUSH tickets, and entering the ticket LOTTERY. RUSH refers to the process of obtaining tickets on the same day as a show, whereas LOTTERY refers to entering (in advance) a drawing for a show that may be one day or a few days after the lottery. Lotteries tend to be digital, which increases access but may reduce your overall success rate, whereas rush can be either in-person or digital. Each show on Broadway differs in whether it offers rush, lottery, or both, as well as in what the price of tickets are obtained in each method. Linked is a great resource (constantly updated) for seeing what options are available for each show
The largest Gothic Revival cathedral in North America, and directly across from Rockefeller Center. The most beautiful building in Manhattan. Go inside and be transported straight to Europe (seriously---you would not BELIEVE you are still in Manhattan).