Fraunces Tavern (Broad and Pearl Streets) was the meeting place for the Sons of Liberty in the run-up to the RevWar. Sam Fraunces was a half-white, half-black tavern owner who eventually became George Washington's guy in charge of the Presidential food and drink when in NYC for the 15 months when NYC was the nation's capital. His famous Farewell to the officers took place on the second floor there in 1783.
St. Paul's (Episcopal) Chapel (Broadway at City Hall Park) was the "uptown" extension of Trinity Church. Since Trinity was burned during the war and had not been rebulit by the time of Washington's inauguration, St. Paul's was where he attended Mass and you can still see the pew he and Martha sat in. The first Presidential Seal remains over the pew. Amazing site.
Morris-Jumel Mansion (Roger Morris Park, 160th St and Jumel Place) was the General's headquarters when the Continental Army was chased from lower Manhattan. From the second floor balcony, the General watched NYC burn.
And there's so much more...
I visited there a few months ago and was impressed. It's miraculous that the building survived the WTC collapse. The church was used during the WTC recovery effort as a place for rescue workers to rest both physically and mentally.