The correct audience is extremely important to a pun. If you present a pun to a mix of people, you may get some who don't fully understand the pun. People who don't get puns kill the moment.

How Do I Know Who the Right Audience is?

Well, this can be a toughie. You never know if someone might not understand a pun. Generally, you can expect your friends to understand a pun, because you probably have the same sense in humor. Also, it helps if your friends are interested in the same stuff as you. Your sporty friend who is always outdoors might not understand a pun that relates to a video game, or a witty movie reference.