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.

We've got a penchant for a fresh and fruity cocktail, and this raspberry lychee martini most definitely fits those requirements. Pleasingly pink and bursting with sweetness, this drink is brought to ...