Gaynor's Hideaway in 1955.

"Suddenly, thrown off balance and about to fall, he [ Marty, on his makeshift skateboard] reached out — and found himself holding onto the front end of Biff's's car. / "Now we've got the son of a bitch!" Biff shouted. "If he holds on, he's dead, and if he lets go, he's dead!" / Smiling sadistically, he began to push Marty down Hill Street, past Gaynor's Hideaway, where customers had come outside, some still holding their drinks, to view the action."
—From Back to the Future by George Gipe (quote, page 179)

Gaynor's Hideaway was a bar on Hill Street in downtown Hill Valley. It was located on Courthouse Square, on the same side of the square as the Essex Theater, in 1955, and later in 1985.