The Prologue to the play specifically mentions the city.
Two households, both alike in dignity,
In fair Verona, where we lay our scene,
The adjective "fair" suggests that Verona is a beautiful city. It could also be a symbolic reference to its inhabitants. One can infer that the city dwellers are reasonable people who are obedient and law-abiding. The word "civil" in the Prologue accentuates the fact that the citizens of the city are ordinary, well-mannered individuals. However, their peace is disturbed by the ongoing battle between the houses of Capulet and Montague. Members of the two houses are consistently at each other's throats because of an age old feud.
Many commentators suggest that Shakespeare's penchant for setting his plays in Italian locations is derived from the fact that many of his contemporaries had a lively interest in the country. Many Elizabethan travelers had gone to Italy as tourists, and it seems as if the Elizabethans were fascinated with the country. Italy had an air of mystery and romance about it that intrigued the Elizabethan public.
By choosing Verona as the setting for arguably his most famous tragedy, Shakespeare catered to Elizabethan society's taste for mystery, romance, and drama. His audience, then, must have been absolutely fascinated by the intrigue - even more than we are now. As it is, the play's popularity, then and now, has encouraged thousands to visit the city in an attempt to recapture, in some way, what Romeo and Juliet's lives would have been like.
The name of the city where the play takes place is Verona. It is a city in Italy. You can find this out in the Prologue to the play. In the second line of the Prologue, it mentions the city and the basic ideas behind the plot.
The Montagues and the Capulets are two of the more prominent and important families in the city. But they are not the rulers. The city is ruled by a prince who is not very happy about the feud that has been going on the between the two families.
The city of Verona in Italy is frequently mentioned; I believe it is in the second or third line in the play. Several of Shakespeare's plays center around Italian cities such as The Merchant of Venice, another city in Italy. The totality of the plays covers the vast majority of the area of Europe during the Renaissance period.
One of the principal reasons that Shakespeare situated his plays in numerous areas was for the different population segments that his audience members were. They came from all backgrounds and all lines of employment. They had various types of educational background, but they all loved a good story in a far away place.