Romeo and Juliet was set in the 14th Century (the 1300s) in Verona, Italy.
The earliest performance of the play that has been documented was 1662; however, there is other evidence that the play was performed as early as 1591. This is a fairly big difference, nearly 30 years! Unfortunately, there is simply no one record still in existence that says the play debuted on a specific date in a specific place.
According to the British Library :
Romeo and Juliet had certainly been performed by 1597, when the first quarto was published. There are no surviving records for any performances before the Restoration in 1660, but it is likely that Romeo and Juliet was first acted by the Lord Chamberlain’s Men at the Theatre and then at the Curtain. It has been suggested that Richard Burbage may have played Romeo, with the boy actor Robert Goffe as Juliet.
In Shakespeare's time it is important to remember that females were not allowed to act, so the roles of Romeo and Juliet would have both been played by men. Juliet's character would have simply been a man dressed in female clothing and make-up. While this sounds strange to us today, and would significantly change the story line for us, for them it as completely normal.