Ugly neighborhoods surround most airports, but as we drove out of Dubrovnik’s, the landscape immediately turned dazzling. After flying nonstop with United from Newark, we headed south through Croatia’s verdant Konavle Valley, sandwiched between the sea and a sheer mountain wall. It took just half an hour to reach the Kobila border crossing with Montenegro.

Though only about the size of Connecticut, Montenegro is utterly packed with treasures. Many think of the country (if they think of it at all) as a brief add-on to the end of a Croatia itinerary, which it can be. But Montenegro also stands alone as a destination. I bustled my traveling companion around on an action-packed week that included walled Venetian cities, abandoned Austro-Hungarian fortresses, sandy beaches, mountainside wineries and a fjordlike bay dotted with islands.

The joys of Montenegro are no secret to Europeans, who now flock to the scenically spectacular country. The robust tourism has encouraged the opening of several luxury resorts along the Adriatic. The (currently closed) Aman Sveti Stefan used to be the only game in town, but no longer.