Back in 1955, Marty discovers the stone "Lyon Estates" gates that will mark the entrance to his home street in 1985. In 1955, however, it's just empty land. And empty farm land isn't easy to find in modern L.A. So, this scene was shot in the town of Chino, CA.
Having gotten a phone call from Doc Brown asking him to meet him at night at the Twin Pines Mall, Marty shows up and is introduced to the DeLorean and some Libyan terrorists. This is indeed a real mall (the name is fake) called the Puente Hills Mall, located in the City of Industry.
We see Marty and his group ("The Pinheads") try out at an audition for a "Battle of the Bands" at McCambridge Recreation Center. They are too much or the adult judges, who pronounce them "Just too loud."
In 1955 Marty goes to "Hill Valley High School" which is an actual high school, but it's located 30 miles away from the film set. In reality, it's Whittier High School which is best known as home to former President Richard Nixon.
The fateful site of Doc's supposed murder at the hands of plutonium-hungry Libyan terrorists and where Marty time-travels back to 1955 isn't the Twin Pines Mall but the Puente Hills Mall in California.