Kotor
You'll be rewarded if you set your alarm for an early start when arriving in Kotor. Part of the fun is entering the Bay of Kotor and gliding for an hour through the mountains on a 17-mile waterway known as Europe's southernmost fjord. It's not actually a fjord -- fjords are caused by glacial activity, and the Bay of Kotor has been carved by a river running from the interior to the Adriatic Sea. Still, the views are fjord-like, with mountains rising on both sides of a long, thin bay that leads to the old walled town of Kotor. Cruise ships often begin the bay journey as early as 6:15 a.m. for an 8 a.m. arrival.
Its fortified entrance to the sea made the Old City of Kotor an ancient trade center. Now it's a UNESCO World Heritage Site and Montenegro's most famous town. The Old City is a well-preserved collection of buildings, churches, squares and stone streets that date to the Middle Ages. The car-free, walled town is just across the street from the city's cruise ship dock.
Kotor is full of shops and little restaurants. Pick a square, order a coffee and gaze at churches from the 12th to 15th centuries.
Looking for more great views? Put on your walking shoes for a hike. The city walls climb the mountain behind the town, and it's about 90 minutes up to the fortress at the crown (at 853 feet) and back.
If your ship is in port for just a few hours, you may want to concentrate only on exploring the Old City. If you have all day, consider excursions into the mountains for sightseeing and stops at seaside resorts on the Adriatic.