Joe Montengna says in the DVD Bonus footage (On Location - A look Inside) that while filming the opening of GFIII at Old St Patricks Cathedral in Little Italy, FFC told him that this was the same location as the Baptism scene in GF1. Hence the "Challenge" in "filming locations" below should be put to rest and removed! Also, I don't see filming locations for GFIII? Here is one.
"Old St. Patrick's Cathedral on Mulberry Street was used for the christening scene. A real Bishop was used. Coppola's family is used as extras. [Challenged: Mt Loretto Church in Staten Island?] "