The Building

Near the beginning of the movie you see Robert Redford get out of a cab and walk up to the building. There is a place called the Earle Hotel next to the building he goes into, and a park in the block behind him. The Earle Hotel is now called the Washington Square Hotel which is located at 103 Waverly Place in the West Village. This means the actual building is in the 100 block of Waverly Place, which is a one-way street heading west.

It's the same building Mildred Natwick goes into when she gets out of the car with the same Hotel Earle next door.

Using Google Earth, you can see a high detail aerial photo of the former Earle Hotel and the building next to it used in the outdoor location scenes. This aerial view doesn't show skylights at all, much less skylights with a broken pane.

The park you see is Washington Square Park. This is the park Corey is referring to when she wants to walk barefoot in. The scenes where Redford is drunk and barefoot, you can see the benches used in the film still in Washington Square Park. Near the end of the film Jane Fonda run under the Arch de Triumph in Washington Square Park.

However, 37 minutes into the movie it's a different building and you can tell it's on a studio backlot, and it's a two-way street. 45 minutes into the movie Mildred Natwick is running in the dark in the rain, and it's on the studio lot with the two-way street. The scenes where they are heading to the restaurant in Staten Island and returning home are also filmed on the studio back lot.

So the answer to your question is: 100 block of Waverly Place, Greenwich Village!