During the 16th century, many English dramatists and poets adapted a wide range of Italian stories and poetry to create their own material. The availability of these sources reflects the English interest in Italian culture during this period as the influence of the Italian Renaissance spread. The term Renaissance means "rebirth" and refers to the period after the Middle Ages when a revival of interest in classical Roman and Greek culture emerged. Beginning in the mid-14th century in Italy, the Renaissance was a period of rapid discovery and development, gradually moving northwards across the rest of Europe.
One Italian source that Shakespeare draws upon in Romeo and Juliet is Francesco Petrarch, 1304-1374, an Italian scholar and poet, who was responsible for developing the sonnet. The poems, which Petrarch wrote for the lady he admired, describe the process of falling in love and courtship, according to medieval ideas of courtly love and chivalry. Translated into English and published in 1557, the sonnets were extremely popular, so English sonnet writers imitated and developed Petrarch's conventions. Source: https://www.cliffsnotes.com/literature/r/romeo-and-juliet/about-romeo-and-juliet
William Shakespeare set a third of his plays in Italy. Take a tour of Verona, Padua and Venice -- three fair cities in which he laid his scenes. Source: http://www.bbc.com/travel/story/20120416-shakespeares-italy
Like most of Shakespeare's plays, the setting is so vague that theatrical and film interpretations of the play can go wild: from West Side Story's 1950s New York City, which is divided by ethnic tensions, to the futuristic "Verona Beach" of Baz Luhrmann's film version of Romeo + Juliet. What most interpretations keep is the sense of a hot climate that provokes the passions, as Benvolio tells us: "For now, these hot days, is the mad blood stirring" (3.1.4). Source: https://www.shmoop.com/romeo-and-juliet/setting.html