Nicole Kidman didn't want to open her latest movie, the period psychological thriller "The Others," just anywhere. "I requested the first premiere be in New York," she told PEOPLE on Thursday night amid the klieglights, "because I really like David Letterman, and I wanted to visit Dave." And visit Dave she did, on the "Late Show," and referring to her height-impaired soon-to-be ex, Tom Cruise, on the program, quipped to the host that it is now safe for her to wear high heels again. (Coincidentally, Cruise is one of the producers of the film, though all that came to pass before the couple's estrangement last February. It has been reported that he will show up at next week's L.A. premiere.) Kidman, 34, arrived at the New York opening with the film's director, Alejandro Amenabar. "The film is in the horror genre," she told PEOPLE, "but it has a great female role. That can be hard to find." She added that she's something of a horror-flick chick. "I used to love to sit up at night and watch scary movies with my dad and eat popcorn," she admitted. "I love to go to a good scary movie where you really scream. I thought it would be fun to do one."