The only Japanese pun/joke I remember learning when I was studing Japanese (30 years ago...) was something to do with hashi (chopsticks) and hashi (bridge). Or was it the poetic one with hana (nose) and hana (flower)? Or tyoo-tyoo (chō-chō) (town mayor) and tyoo-tyoo (butterfly)....

Of course it's nothing like so funny when you see the kanji, because they're different....