All I can remember is that the movie ended the with the main characters underneath a small bridge with a bomb or missile about to destroy the city in order to get rid of whatever creatures were attacking the city.
This movie ends as you described in your question.
Quote from Wikipedia:
“The man then tells Rob when the last evacuation helicopter will depart before the military executes its “Hammer Down Protocol,” which will destroy Manhattan in an attempt to kill the monster.”
“Moments later, Rob, Beth, and Hud are taken away in a second helicopter and witness a U.S. Air Force B-2 Spirit bomb the creature.”
“Rob and Beth grab the camera and take shelter under Greyshot Arch in Central Park. As sirens blare and the bombing starts, Rob and Beth take turns leaving their last testimony of the day’s events. The bridge crumbles and the camera gets knocked out of Rob’s hand and buried beneath some rubble. Rob and Beth each proclaim their love for each other just before another bomb goes off, with both screaming while the monster roars.”
I am pretty sure that this is the movie you are looking for. If you agree, then please select my answer above as Best Answer, there is an option for that.