Pokey

MICHEL: This is a felony, you know, corrupting a minor. We’ll all end up in the pokey [for trying to get Rory into a nightclub].
RORY (imitating Michel’s pronunciation): He’s right. We’re all going to the pooky.
LORELAI: Sweetie, don’t say “pooky”. It’s creepy.

Pokey is American slang for “gaol”, dating to the early 20^th century. It’s a variant of pogey, 19^th century British slang for a poorhouse.