Openssh sshd by default accepts these environment variables from the client:
AcceptEnv LANG LC_*
You can use that to send a value from the local environment of the client to the server like this:
LC_CDPATH=/var/www/websites ssh -o SendEnv=LC_CDPATH user@server
You can place the SendEnv directive in ~/.ssh/config so you don't have to include it on the command line.
If you place the following in your ~/.profile (to only affect interactive logins use .profile, to affect all logins use .bashrc):
if [ "$LC_CDPATH" -a -d "$LC_CDPATH" ]; then
Then it will automatically change directory to the one specified in the environment variable when you login, if it is specified and if it is a directory.