This is Quince Alley, which sits between South Water and South Front streets. The building on the right has been several different restaurants. This was shot from near Water Street and looking down the alley toward Front Street. The building in the background is still there with the same structure, which is what is shown on the map below:
This location serves as a conflict zone in which the boys all get serious with each other. Dinger (Corey Haim) and Derek (John Ward) show up to find Joel trying to exact lethal revenge on Dumas (Matt Adler) and his gang.
Positioned on top of the car hood, Bobby/Coleman (Corey Feldman) and Lainie (Meredith Salenger) are just across the river from where so many montages were shot for this movie. That large building is the Alton Lennon Federal Building, which the horse-drawn carriage dragged past with both this couple and Coleman with Gena. The small building to the right is the restaurant also used by both. This is shot in the grassy area behind the parking lot of the Battleship North Carolina tourist site.
On the field, Bobby (Corey Feldman) faces off with Dumas (Matt Adler), while the sidelined Dinger (Corey Haim) does his best disco moves.
This was a puzzler for me as New Hanover High School doesn’t have any fields around it, as it is in an urban setting surrounded by houses and buildings. But then I saw the *barbed wire* fence surrounding the field, not something a school would have, so it must have been a private field. Then I saw it, the odd but distinctive tall brick structure which I’ve long believed is used for fire training, and I knew exactly the location, it had to be Legion Stadium. Mystery solved!