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Mel Gibson and gal pal Oksana Grigorieva heading into Balthazar for lunch yesterday ... Jessica Simpson leaving the Ritz-Carlton in Midtown ... John Mayer walking around downtown ... Ivanka Trump arriving at a book signing at Barnes & Noble ... Kelly Rutherford heading to the set of Gossip Girl on the Upper West Side while Blake Lively and Chace Crawford talk on a bench nearby ... Matthew Broderick walking son James to school in the West Village ... Celine Dion leaving the Ritz ... Chris Pine walking by himself ... and Sarah Jessica Parker making her way to the set of Sex and the City 2 with a bunch of fans following behind her.