TriBeCa is Robert De Niro’s turf, so it’s only fitting that the movie star who grew up in this New York neighborhood already has two restaurants, his own film center, and a hotel here. The Greenwich Hotel sticks to its roots, exuding the same sophisticated, relaxed chic so popular in TriBeCa. Guests feel like they are visiting some well-traveled friends who have decorated their place with trinkets from around the world. Pieces such as hand-woven silk carpets from Tibet and tiles from Morocco decorate the 88 rooms, of which no two are alike.