I would love to meet JK Rowling! obviously, she's one of the best children author in the world!
I would love to meet her any place when she's not busy, so that i could talk to her for ever. I bet she would be really annoyed with me after our conversation, because it would have taken about 6 hours for me to ask her all the questions I want to ask her....
I would ask her stuff about HP:
-What happened to Umbridge in the end?
-Did you always know Cedric was going to die?
-Did Molly use the killing curse on Bellatrix?
-Were there any consequences for the unforgivable curses Harry used in the 7th book?
-How come the Malfoys didn't serve anytime in Azkaban?
-Where was Dumbledore during the 5th book, when he had to leave the school while being looked for my Ministry of Magic officials?
-Did Victor Krum ever find true love?
-Who was headmaster at Hogwarts when Harry's kids attended the school? etc, etc...
But I would also ask her things like:
-What was your reaction when you found out the Warner Brothers wanted to make HP into a movie?
-How did you get the idea for Harry Potter? etc, etc,...
I would also like to know her opinion on the movies and other HP related stuff:
-Do you think the actors are good?
-Did you imagine Snape to be like the way Alan Rickman plays him, because I think he's perfect for the part?
-Which Dumbledore actor do you prefer,and why?
-Does it annoy you that they had to cut out so much of the books for the movies?
-What are your feelings about the HP electronic games? etc, etc,...
As you can see I would throughly pester her with all the questions I have ever had about Harry Potter.