To make your life easier, you can make a simple change to the MySQL configuration file /etc/my.cnf that will permanently set the socket file used by the mysql client. After making a backup copy of /etc/my.cnf, open it in your favorite editor. The file is divided into sections such as

[mysqld]
datadir=/usr/local/mysql/data
socket=/var/lib/mysql/mysql.sock

[mysql.server]
user=mysql
basedir=/usr/local/mysql