Steve Morse's site https://stevemorse.org/
contains all the links you'll need to search for NYC marriages, and much more.
Some links are for marriage index only, others contain some transcripted data from the record.
During some years the names of people applying for marriage were listed in the newspapers.
Try searching the name of the bride or the groom here: https://fultonhistory.com/Fulton.html
It is a free site of old digitized newspapers, many from NYC.