Steven's Quarry is located just outside of Mystic Falls. It is the place where the sacrifice took place, where Stefan and Damon woke up after their transformation, and Stefan thought of committing suicide here.
In 1864, both Stefan and Damon came back to life as vampires. Emily and her brother brought them here, and she let them know they were in transition and that if they did not feed they would die. In Blood Brothers, after Elena let Stefan escape from the Salvatore basement. He goes to the Quarry to wait for the sun to rise but Elena saves him and give him the option of throwing his ring in the Quarry or staying to keep fighting.