I'll start!

Alfred's has live music every Sunday, Tuesday and Friday.

Bourbon Beach has live music pretty much every night, but Saturday night is a big time party.

Boat Bar on Friday afternoons for live music -- usually Naggo Morris sings.

I believe Three Dives has live music on Tuesdays, but you may wanna confirm.

Not live music, but try to make it to Sir D's Firewater Love Nest on the cliffs for a sunset while you're there -- it's pretty amazing.