This 1903 footage was taken on "a boat heading south along the eastern shore of Blackwell's Island, known as Welfare Island from 1921 to 1973, and as Roosevelt Island today." According to the YouTube poster: "The film opens showing the lighthouse at the north end of the island (Hallet's Cove)... the following buildings, in order of appearance, are seen: the New York City Lunatic Asylum [0:39]; the Workhouse; the Almshouse [0:45]; piers for the Queensboro or '59th Street' Bridge still under construction, which upon completion in 1908 will span 135 feet above the island [1:20]; the Almshouse Keeper's House (originally the home of the Blackwell family, who had once owned the island) [1:30]; the Penitentiary [1:45]; Charity Hospital [1:55]." By the end of the 2:27 clip, you'll have reached the southern tip of the island.
Prior to being called Blackwell's Island (which was the DOC's island home before Rikers), it was called both Hog and Manning's Island. The city didn't purchase it until 1828 (for $32,000). Today, the Blackwell House is the island's oldest landmark. [via Roosevelt Islander]