Flavio, I will second Jodi's recommendations- especially the Ferry.  Don't wait in line for things like the Statue of Liberty or the Empire State Building unless you have time as they eat into your day. 

Washington Square Park is nice.  See it before NYU completely overbuilds around it. And while it's hardly a tourist attraction, I always recommend the Upper WEest Side which is the general area I live in as it's a glimpse of non-touristy things and shows New Yorkers on their day to day.

And Jackson Heights in Queens will blow your mind.

Flavio the little Church beside the 9/11 site is really cool too. It is where Washington went before being sworn in. Also Ed, who is an amazing tour guide BTW,  took me to Wall Street, which is really cool.

Having been to NYC once, I'm far from an expert, but my two daughters are now there for University so I have a mixture of first hand (below) and second hand (I'll quiz them tonight and update this post)recommendations:

Metropolitan Museum of Art -- Located on the east side of Central Park, this is a spectacular museum with a little bit of everything. I would plan a day to see as much as possible, and stop for lunch at their French Cafe.

Museum of Modern Art -- This five story museum spans the gamut from awesome to "Really...?". The top floor has some fantastic works by Monet, Van Gogh and Dali. That one floor is worth the price of admission.

Grand Central Station -- Spectacular building, great place to people watch, and plenty of dining choices for any budget.

United Nations Building -- Just a couple of blocks east of Grand Central Station, this was a fun place to visit. Take the guided tour of the facility, which includes the General Assembly and the Security Council, and their museum.

And as you walk from Grand Central Station to the UN, you'll pass the Chrysler Building and -- perhaps more importantly -- the NY Daily News Building, where you can walk into the lobby, see the giant globe and suddenly realize this was where they shot the Daily Planet scenes from Superman. (That was an accidental discovery we made while passing by -- I knew they'd shot at the Daily News Building, and I had it on my list of things to look up before stubbling on it -- that thrilled my Superman loving-daughter and her Superman-loving old man.)

And, of course, the all important comic book store recap:

Jim Hanley's Universe -- Located across the street from the Empire State Building, I found this store to have the most extensive stock of the stores I visited.

Mid-Town Comics -- I visited two of their locations, one a couple of blocks north of Grand Central Station and the other off Times Square, and found them to be well-stocked stores.

Forbidden Planet -- Located near Union Square, this one the store I'd heard most about, but found it the least impressive. BUT it is right next door to an incredible bookstore, The Strand, which if you like to wander around new and secondhand bookstores I highly recommend.