The John Street Methodist Church is the OLDEST Methodist continuing congregation in this country and still has the clock that John Wesley gave it, when the first building was consecrated by him or Charles..I forget which one. And yes, they have the usual fellowships, even though it's situated in the Financial District.
In the same area, there's Trinity Church, which is Episcopal and was begun in Colonial times as well. Many of our well known FFs are buried in their cemetery.
Up town, is SAINT PARTRICK'S CATHEDRAL ( Roman Catholic ) on Fifth Ave.
And all over Manhattan there hundreds of neighborhood churches of all kinds!
And yes, when I grew up and lived there as an adult, whilst I didn't know ALL of the people in those different neighborhoods, I knew many of them and NOT only the ones who lived in the same building. Heck, I even knew some of the people, when I was an adult, who lived in my parents' building and neighborhood.
Decent schools are hard to find, NOW, no matter WHERE you live. Then there is SAINT JOHN THE DEVINE, farther uptown and is an ANGLICAN Cathedral.
So SORRY for the messed up end of it!