There were several, it seems.

Here is good information about Delmonico's at Fifth Ave and East 44th Street. It was designed by James Brown Lord and opened in 1897. The kitchens, larders, refrigerating rooms, butcher shop and other culinary departments were housed in the two floors below street level. On the ground floor were the ladies’ restaurant and the palm garden and Elizabethan-style cafés. On the second floor were private dining rooms. A Louis XVI ballroom engulfed the eastern half of the third floor and on the Fifth Avenue side was the “supper room.” The top two floors were income-producing bachelor apartments. Above it all was a roof garden which would be enclosed by a vault of glass 30-feet high in the winter.

At the corner of Fifth Ave and East 45th Street is the still standing 545 Fifth Ave, designed by Jeremiah O'Rourke and opened in 1898 as the Hotel Lorraine. In 1930 it was converted to an office building.

To the far left you see vuvuzela-bearing angels atop the Church of the Heavenly Rest. It was a large, L-shaped church, whose congregation included many prominent names. Future president Chester A. Arthur and his wife, Nell worshiped here.

For we lived by blood and the right of the might
Ere human laws were drawn,
For the age of sin did not begin
Till our brutish tusks were gone.
And that was a million years ago
In an age that no man knows,
Yet here to-night in the mellow light
We sit at Delmonico's.

'Harper's Weekly' threw a 70th-birthday dinner for Mark Twain in Delmonico's red ballroom in 1905. It was a very big deal, with 170 invited guests, a 40-piece orchestra, and a foot-high plaster-of-paris bust of Twain for each attendee.

This Fifth Avenue location of the venerable restraurant opened in 1897, in an attempt to counter the growing popularity of the Waldorf-Astoria for grand events in the mansion district.

Below is the same view from June of 2009.