New York Public Library is a famous movie spot. Ghostbusters, Sex and the City, Oblivion and many others are the proof of it. Definitely worth visiting!
Al Schant's restaurant, has been a famous New York spot for a long time. Unfortunately for Breakfast at Tiffany's fns it's closed now. However, there are other restaurants in the area, so you definitely won't stay hungry!
Pass by Park Avenue fountain
The most famous scene from the movie. To copy the moment go there early in the morning (you will also avoid a huge crowd of people), grab a croissant and coffee, stare at Tiffany & Co and then continue your movietrip :)
You might also go inside and have a walk around Tiffany & Co
Walk down by E 71st St, to get to Holly Golightly's Apartment
The famous building where Holly Golightly lived
Conservatory Water is a natural hollow in the Central Park, not so far from 5th Avenue. Have a nice walk!