According to Production Weekly Men in Black 3 is scheduled to begin filming in New York City on September 13th and will finish after a 3 month shoot around New Years Eve. This means they will have over a year and a half of post-production as Columbia has given Men in Black 3 a release date of May 25th 2012.
Not a whole lot is known about the film, other than it will be in 3D. David Koepp (Spider-Man) is currently rewriting a new draft of the script which takes place primarily in the year 1969 as Will Smith and Tommy Lee Jones are transported back in time where they meet Josh Brolin, who plays a young version of Jones. Jemaine Clement from Flight of the Conchords will play the villain, although his motives have not been revealed yet.