I asked someone on IMDB who said his/her brother is Ben Foster’s stand-in in ‘The Mechanic’, where they are shooting in New Orleans and I got this answer back.  This is the closest we can get to finding out about the filming locations for the movie.  The reply is from yesterday (Thursday).

they’ve been filming here and there in the french quarter downtown. tomorrow, and i suppose off and on, they’ll be filming in covington, for statham’s character’s house – interior shots. and various spots up and down the river so far.