Hillside Cemetery is located in what was referred to as Peekskill, but was actually the Town of Cortlandt. It is now known as Cortlandt Manor, Westchester County, New York on Oregon Road, right next to the Old Van Cortlandtville Cemetery (St. Peter's).
[The cemetery is a] large rolling hill with multiple sections, encompassing Old St Peters Church Yard, abutting Old Van Cortlandtvill Cemetery on the South and Assumption Cemetery on the north.
https://www.findagrave.com/cemetery/64829/Hillside-Cemetery
Around 1750, a plot of land of about 4 acres was set aside for a church and burial ground. In 1770, by royal charter, this tract was assigned to St. Peter’s Church. The church graveyard served as a burial ground for all of the Town of Cortlandt, which included Peekskill, and it became crowded as the local population grew.
Hillside Cemetery had its beginnings as a separate cemetery in the 1850s, as land bordering St. Peter’s church graveyard was acquired for use as burial space. It was incorporated as Cortlandt Cemetery Association in 1884.
http://hillsidecemeterywestchester.org/