Where did The Beatles make their first appearance?

In 1959, as the Quarry Men, they started playing at the Casbah Club in Liverpool which was run by Pete Best's mother. In 1960, as The Beatles, and with Pete Best as drummer, the played at the Indra Club in Hamburg for 48 nights, then at the Kaiserkeller for a further 58 nights. On their return to Liverpool, they play at the Cavern Club, followed by a return to Hamburg at the Top Ten Club, then back to the Cavern Club which is where Brian Epstein sees the Beatles for the first time, and the rest is history.