To send a fan mail via regular mail you can use the addresses bellow:

Miley Cyrus
c/o The Disney Channel
3800 Alameda Ave
Burbank, CA 915058

Miley Cyrus
P.O. Box 1459
Santa Box, California 90406
USA

Thanks a lot to Patrick and Rachel for the info!! The source of the snail mail address is Fanmail.biz.