Here are a few restaurant recommendations near the area you are staying:
Marta (Italian, Traditional thin crust pizzas) <-- very good personal pies in a restaurant setting. not slices.
https://goo.gl/maps/aBd68BKPXwy
L'Amico (American w/ French/Italian elements) <-- the have pizzas but this place is great for brunch & cocktails
https://goo.gl/maps/Zn9Q6YaQNVP2
Hillstone (American) <-- classic, but very good. Burgers, fish, etc. Haven't had a bad meal here, to be honest.
https://goo.gl/maps/CXr6qqbMhNG2
Maialino (Traditional Roman cuisine)
https://goo.gl/maps/7j9LXgxZ4FC2 <-- Haven't tried this place yet, but it's on my list of "must-try" in NYC.
Classic Midtown slice:
NY Pizza Suprema:
https://goo.gl/maps/PUg8VZwWdAG2
A long 4 avenue block walk west from Madison on 31st street. This is probably one of the best traditional NYC slices your going to find anywhere in Manhattan. Simple, easy, order, pay, sit and go pizza joint, but one I can vouch for.
Statue of Liberty... even if the tours to go in are booked up, you can still easily hop a ferry last-minute and go walk around the island. It's nice even if you can't go up in the monument. Otherwise, save your time with the Staten Island ferry... no point, honestly. You'd get just a good of a view from Battery Park in downtown or Liberty State Park in Jersey City. If you wanted to do a fun boat tour where you see a lot and learn about the city, go with the Circle Line Best of NYC tour:
https://www.circleline.com/sightseeing-cruises?locale=en. I've done it myself and it's very informative. I learned a ton about the city, stuff I never had a clue about. Also, they have some Statue of Liberty tours on that link, including ones that leave from midtown and downtown.
Pizza, pizza, pizza... I wouldn't suggest just stopping off at just any corner spot, but I'm picky about my NY pizza because I grew up there. You just don't know anymore because a lot of places are getting away with duping the tourists with lazy and crappy "NYC" pizza using cheap ingredients. I honestly could go on and on with recommendations of the best places to get pizza, but it would be a lot easier to just give you the spots I know based on the neighborhoods you plan to visit. You can list them here, but even if you're over there during the weekend and you post in this thread that you're going to be in "such and such" neighborhood, I can just give you one or two restaurant/pizza suggestions that I highly recommend in that area.
As for the downtown-9/11 memorial area, since I know you're visiting, I wouldn't exactly recommend many pizza spots around there, but I would suggest the following:
Stone street
After you are done visiting the memorial (or before, depending on your timing), walk over to/from Broadway and head south. Hang a left on Wall Street and then your second right south on Broad St. You'll pass right in front of the NYSE, where you can take some photos. Then make your first left on Exchange Place to get back onto Broadway going south again (left). You'll pass the iconic Charging Bull where your can take some pictures and then keep heading south towards the Customs building... can't miss it as Broadway dumps right into it and Battery Park. If you have the time, there's a great exhibit inside the Customs house and the walk around Battery Park with views of the harbor is nice as well. You can also catch ferries to Liberty Island, etc from the park. Anyway, back to where you can find a good meal in downtown... Once your walking past the Customs House which will be on your left on Broadway, make a left onto Stone Street. You want to continue on Stone, but it gets cut off by the 85 Broad St building, so you make a quick left and a right onto Broad and then William. Walk around 85 Broad (tall brown building) and look for umbrellas with outdoor seating for restaurants out on a small street. This is the old Stone Street that is lined with great places to eat outside and enjoy a historical part of downtown. You can't really go wrong with any of them, I've tried most. You can even get a decent pizza at Justinos or Adriennes. Good coffee and pastries at the Financier... you can figure it out on your own, but its just a nice area and you'll understand why when you get there. Also, if you have any desire to treat yourself to a good steak, go to Delmonico's, which is right around the corner (56 Beaver St). It's on a historic intersection that includes the "bank" building (20 Exchange Place) where they filmed the movie Inside Man with Denzel Washington. Here's a map of the walk I just described, which may be a bit easier to follow:
