If there is room for one more response to this interesting assignment, I would add this:consider writing the letter from the point of view of one of the characters, such as Juliet. Using bits and pieces of Juliet's language in the play to make the letter seem authentic, she might ask her creator some pertinent questions as to why he has her do certain things, who she reminds him of, and so on.  Juliet might even express her displeasure at having to die at the end of the play, explaining that she would have preferred to live for that would have provided a different meaning to the play (you figuring out what the play would be like if, say, she lived but Romeo died, or she died but Romeo did not.  Choose one or two or three passages from the play and, in the voice of Juliet (or another character) express your approval or disapproval of the way Shakespeare wrote them, asking him questions in the process.

You don't say if the letter should be related to Romeo and Juliet  only or all of  his plays. I would certainly ask some questions about Shakespeare's personal life, such as:

How did you become interested in writing and acting?
How did the death of your son, Hamnet, affect you and your writing?

Regarding the play of Romeo and Juliet, I would ask him if he believes in fate or love at first sight? Tell him what you liked and disliked about the play. Do you think the play should have end the way it does? You might suggest an alternative ending.

Well, as a teacher, I can't write it for you, but I will gladly give you some ideas that I would like to see from a student.  The best place to start would be to ask any questions that you may have about the play and/or Shakespeare. For example, where did he get the idea for the play?  A question that I have always had is why couldn't Friar Laurence have waited for Romeo or at least have found some more definite way of getting the message to him that Juliet was still alive. Another question, why did he allow Friar Laurence to marry two children so young no matter the motive or his good intentions? You know the old saying, the road to hell is paved with good intentions. I know it all falls back to plot, but sometimes you have to wonder when and where common sense comes into play with characters, you know? Didn't mean to rant; anyway, I hope this helps. Brenda