You've heard about the reading room at the New York Public Library, haven't you? Then I need not go on. Just look at it. And you're allowed to hang around in there!
Beach approachable by public transportation and can be connected with a visit of MOMA PS1 Art Installation (Katharina Grosse House) Also less crowed than other beaches in NYC.
not only as an Austrian you are sometimes craving sausages - the "Wurst Case" Car parked in front of Diviera Drive is as photogenic and good as the place itself!
An awesome, and sometimes free, ferry that links Manhattan at the Financial District to Ikea in Brooklyn via Red Hook. Very great views of the city and if you end up having to pay it's redeemable for a monetary discount towards an Ikea purchase. I think of it as a treat and an investment.