Possible Clues:

• Dance involving drink to some degree
• It's strange, baby: bygone music
• Odd university degree given for Dance
• Drink's plonked on bar -- short -- in a Havana 6 down
• Republican comes to the fore in shadow dance
• A little comfort, heading off to a dance
• Cha-cha cousin
• Ballroom favorite
• Are you listened to by the doctor, a Cuban export?
• Steps off the wall, twisting stomach muscle