Believe it or not, I think one of the best things to do in New York on a Sunday afternoon is to go to church.
I'm a member of the Church of Jesus Christ of Latter-Day Saints and we have meetings at several different times and locations. There are several chapels in and around New York City and we welcome anyone who wants to come. I'm not from New York, but I'm going there for a work seminar and then I'm staying over the weekend with my wife, so I'm looking for a chapel to go to.
I went to https://www.lds.org/locations?lang=eng and found the location of the closest chapel, congregation, and meeting time.
Here is a great article about 10 Fun Activities For A Sunday Afternoon: http://www.mormon.org/blog/sunday-activity-ideas