Woody's is a long-standing live-music bar on the malecón, run by an American expat who has been in Cozumel for decades. It is a touch cruise-passenger friendly but the bands — usually rock or blues covers — are reliably good and the upstairs balcony catches the breeze.
Beers are reasonable, cocktails are stronger than they look, and the crowd is a mix of locals, divers, and visitors who have figured out it is the best of the strip. Music starts most evenings around 8pm.