Miracle Mile (1988) on Netflix

In Los Angeles, when the musician Harry Washello meets Julie Peters in the museum, he immediately falls in love with her. They schedule a date late night in Miracle Mile, but the alarm clock fails and Harry misses the date and he arrives three and a half hours late. Harry accidentally hears a mistaken phone call and a man tells that the United State has just started a nuclear war sending missiles against Soviet Union and in two hours Los Angeles would be hit by the enemy back missiles. Harry seeks out Julie and frantically tries to find a helicopter pilot to leave Los Angeles. Meanwhile the rumor is spread out and brings chaos to the city.