It's unfortunate you're too late to see Trinity Church before it burned (construction on a new church won't start until 1788). Trinity's a bit of an institution in New York, especially in the late 18th century. The church founded both the Trinity School, and King's College, which later became Columbia University. St. Paul's Chapel is another offshoot of the church. (You can't get a better indication of how Loyalist New York was than that: it had two branches of the same Anglican Church operating within blocks of one another.)
Captain William Kidd (yes, the famous pirate) lent some of his ship's equipment to help build the original church (the one you see here, burned), which was nice of him. Many people these days consider many pirates to have been rather progressive socialists with community-minded consciences, which I rather feel takes away from their mystique. It's like finding out Genghis Khan had solar panels.