According to Juliet's mother it is a fortnight and a few odd days before Lammastide, which is the same as Lammas Eve. Lammas Eve is on July 31st. The Nurse, a tenderhearted and devoted servant but a nonstop talker, tells her:
Even or odd, of all days in the year,
Come Lammas Eve at night shall she be fourteen.
Susan and she (God rest all Christian souls!)
Were of an age. Well, Susan is with God;
She was too good for me. But, as I said,
On Lammas Eve at night shall she be fourteen;
That shall she, marry; Act 1, Scene 3
Evidently the Nurse became Juliet's wet nurse and surrogate mother because her own daughter Susan died the night Juliet was born, thus enabling the nurse to breast-feed Juliet
So the play is set in the middle of July, and Juliet will turn fourteen on the last day of July. It seems likely that the girl was given the name Juliet because she was born in the month of July. This helps to explain why the young people are staying up so late. The weather is balmy and the sun does not go down until eight or nine o'clock. The air is full of the intoxicating blended perfumes of flowers. It is the season for young love to flourish. Shakespeare evidently intended to establish that the season was mid-summer, because the play might have been performed in England at any other time. The season of the year is important because it invites young men to stay outdoors, where they can fall in love, get into sword fights, crash parties, talk nonsense, and sleep late the next day. They own the nights because their elders are all snoring away in their beds.
There is no specific month mentioned in the play. The fact that much of the action takes place outdoors indicates that it is not wintertime. Traditionally, "a young man's fancy turns to love" in the springtime, so it might be spring.
If I'm not mistaken, the play takes place in July. It says so in Act i sc.iii. Juliet is born around August 1st, Lammas-Tide, and the play takes place two weeks before.
It couldn't have possibly been anywhere near 1303 because Shakespeare was born in 1564. I don't know the date though.
I am currently studying Romeo and Juliet at a very prestigious school in a very prestigious schooling system, and we are going into Romeo and Juliet in great detail. In Act I Scene III of hte book, on pg. 35, line 16 of the Nurse speaks of Lammastide. Lammastide is of or around Lammas Day, usually referring to Lammas Eve. Lammas Eve is July 31st, and, when referring to it, the Nurse states it is only "a fortnight and odd days [away]." This means that it is two weeks and a certain amount of odd days away, usually a small amount of days. In my class, we first went back a fortnight, to July 17th, then went back 3 days, as that is an odd number, and so the specific day of the beginning of the play is Sunday, July 14th.
there isnt a specific month but your question helped me answer mine
i dont think there was a specified month for romeo and juliet