Cloverfield (2008)

Rob Hawkins gets a new job in Japan. At the celebration party, a massive creature abruptly attacks the city, causing chaos and destruction. We see the story through the lens of Hud, who records the events as the group of friends tries to survive and find Rob's missing girlfriend, Beth. The movie was praised for its suspenseful sequences and its effective use of the found footage style! With a lot of action and a big badass monster: you can not miss NYC in a dystopian destruction!