Maybe Dublin Deck in Patchogue? It's an outdoors bar/restaurant with a pretty solid tiki/Hawaiian theme going on and live music a lot of nights. Drinks are kind of pricey but their happy hour specials are usually decent, definitely worth checking out, only open in the summer/late spring/early fall though because it's outside.

Another one to check out is Rhum in Patchogue, it's indoors and it's pretty cool, tropical theme with 3 floors and the bar has swings hanging from the ceiling instead of bar stools.

Also if you like Cuban or wanna try it check out Cafe Havana in Smithtown, awesome food and pretty authentic Cuban atmosphere, definitely worth checking out