The Soldiers and Sailors Monument in Riverside Park at West 89th Street, commemorating the New York regiments that fought in the Civil War. Designed by the Stoughton & Stoughton architectural firm (which also designed the 52nd Precinct Stationhouse in the Bronx) and built in 1900-1902, just a few years after Grant's Tomb on 123rd Street, the monument was designated a landmark in 1976.

I haven't found any New Deal connection yet, but the New Deal was all over every other monument in and around Riverside Park so I can't believe they never touched this one. Once I find a definitive answer I'll put the information.

References:

1. Dunlap, David W., “Interior of Soldiers and Sailors; Monument Remains a Hidden Jewel”, New York Times, May 20, 2015.
2. New York City Landmarks Preservation Commission Finding and Designation, September 14, 1976, Number 2, LP-0932.