There is a record inside the jukebox. It is behind a plastic window. Before trying to get the record make sure you visited Pier 69.
This is the low-spoiler guide for "Getting the record" puzzle in Leisure Suit Larry - Wet Dreams Don't Dry. Unlike in normal walkthrough, you get gradual hints on how to solve the puzzle. Click the big button below to see your first hint. If the hint contains a spoiler, you will be warned about it before clicking.