I picked "say-hi-locally" and set it up on my linux server as:
alias say-hi-locally="echo EMIT SAY HI"
Then, since I use ITerm2 as my local terminal, I set up a trigger in ITerm2 with the regexp "EMIT SAY HI" and told that to run the local command "say hi"
Now I can do:
do-something.sh; say-hi-locally
and when it finishes it will echo "EMIT SAY HI" which ITerm2 will then pick up and then my computer says "hi" to me! :-)