In a slinky dress on a balmy May night, "The Bachelor" star Hannah Godwin was making the rounds at a Brooklyn rooftop party with a cocktail in hand: No, not a martini — not even an espresso martini.

Created by the same bartender who first garnished a drink with a mini umbrella, a classically made Blue Hawaii remains delicious. Blue drinks get a bad rap these days. That’s a shame, because the ...