I've managed to get hold of Joanne Rowling's UK and US address. Please note that she is very busy, and it's unlikely that she will reply.
J. K. Rowling
c/o Bloomsbury Publishing
38 Soho Square
London
W1V 5DF
UK
or
J. K. Rowling
c/o Scholastic Inc.
555 Broadway
New York, NY 10012
USA