Jesus was crucified at a place called Golgotha, which is an Aramaic word meaning "the place of a skull" (Matthew 27:33, Mark 15:22, John 19:17). In Luke 23:33, the same location is referred to by its Latin name, Calvary (from calvaria, also meaning skull). The site was outside the city walls of Jerusalem.
While Golgotha was geographically near Jerusalem, it is identified as a distinct named location, not simply "Jerusalem gate." Sinai is the mountain in the desert where Moses received the Ten Commandments, far from Jerusalem. Bethlehem is the town where Jesus was born, located about 10 kilometres south of Jerusalem. The Gospels are unanimous in naming Golgotha as the specific place of crucifixion.