score:6
There are tours designed specifically for this:
Free Tours by Foot gives a few choices like:
Of course that's not the only venue to hear the a gospel choir
Or you can just review the New York Gospel site to find the venue you might like.
Upvote:5
Hillsong has a very vibrant, largely white, church in NYC at W34th St. Info is at: http://hillsong.com/nyc
Redeemer Presbyterian Church is also very vibrant with a large (few hundred) crowd, meets on east side at Hunter College at 695 Park Ave. Info here: http://www.redeemer.com/visit/times_and_locations
These two churches will be much more along the lines of Joel Osteen's Lakewood church in TX, which is much more self-help and inspirational, with a majority white crowd, inspirational music, etc.
For an African-American experience, a large popular church is The Brooklyn Tabernacle in Brooklyn, NY (one of the New York City boroughs, but note this is outside Manhattan and can be reached easily by subway). They are known for their choir, with most of the congregation singing along. They sing for about an hour, then a sermon follows for approx 30 - 45 mins.