Welcome!
The Statue of Liberty is not an all-day thing, but it might take you a few hours (particularly if you're there on a heavy tourist day - just waiting in line for the boat and getting through security could take over an hour). Seeing Liberty Island itself takes as long as you want it to take, frankly...some people just set foot on the island, take a few pictures, and get back on the boat to Manhattan; others like to walk around the island, read everything there is about the history of the statue, etc. If you want to see the whole thing, you're probably looking at an hour on the island.
Ellis Island is on the same boat route as Liberty Island, so if you want to see Ellis Island too, that's pretty easy. And again, that can take as long as you want it to - some people spend a lot of time there; others just walk around for a few minutes and then head back to Manhattan.
No need to schedule this in advance if all you want to do is visit the island, but you do need tickets in advance if you want to go inside the statue and up to the crown. I've never actually done that before, so I don't know the details, but I know there is a website for it.
If you don't care about actually visiting the island itself but you just want an up-close view of the statue, one alternative you might consider is taking the Circle Line cruise around lower Manhattan. It's a one-hour narrated boat tour that takes you around both sides of lower Manhattan, and out around the statue. The narrators are pretty good, and they'll give you some interesting history on the city in addition to a view of the statue. It's a good alternative if you're on a limited time schedule, and you have other things you want to see. Tickets can be bought at Castle Clinton, which is the same place you'd go to buy tickets for the boat ride out to the statue.
After seeing the statue, the 9/11 site is an easy walk north from Battery Park. I doubt you'll spend much time there; despite the significance of the site, there really isn't a lot to see (although it's still under construction and I haven't been there in a while, so there may be more than I'm aware of).
The Empire State Building will take about an hour, unless you're there on a very heavy tourist day (in which case you might wait in line forever for the elevator).
In terms of other things to see - Central Park is nice. Broadway shows are always fun; if you go to the TKTS booth in Times Square, you can usually get discount tickets to any of the shows that've been out a while. If you're into art museums, the Met and the Guggenheim are both worth checking out, as is the MoMA.
You should also go to Times Square at night, just to see the lights and get some pictures.
In terms of food, you have to hit one of the good New York style pizza places (John's on Bleeker Street or near Times Square, or Lombardi's in SoHo). You should also get a corned beef or pastrami sandwich at one of the famous NY style delis (Katz's on Houston Street, or the Carnegie Deli at Broadway & 55th). Katz's is my favorite, and it also has some historical significance as the restaurant where the "orgasm scene" from When Harry Met Sally was filmed, if you care about that kind of thing.
Feel free to PM me if you have other questions, or if you'd like to have a beer while you're here. My office is only a couple blocks from the Empire State Building, so it'd probably be easy, and I'm always happy to chat with a Montanan our here.