Terceira, the third largest island of the nine, has no shortage of dreamy blue water (the Atlantic Ocean surrounds it, after all), lush foliage and larger-than-life hydrangeas of its own.

As party islands go, Terceira is a pretty mild one. This volcanic rock in the Azores archipelago isn’t much like Ibiza, nor Mykonos, nor Hvar. But by Portugal’s decorous standards, Terceira ...