Kotor is the star of the Adriatic coast — a compact medieval city enclosed by 4.5km of Venetian walls, with the Bay of Kotor fanning out below. The old town is genuinely beautiful, with well-preserved churches, cats everywhere (the city has an official cat mascot), and a market under the walls selling dried figs, mushrooms, and olive oil. It's also a popular cruise port, so aim to be there in the morning before the ships dock.
Budva is the main beach resort, with a photogenic old town on a small peninsula surrounded by water. The beaches south of town are better than the crowded strip in front of the hotel zone. In summer it is loud and packed; in May and September it is considerably nicer.
Sveti Stefan is the image on every Montenegro postcard — a turreted village on a tiny island connected to the shore by a narrow causeway. The island itself has been a private hotel since 2007 (Aman Resorts; very expensive). But the mainland beaches on either side are public and excellent, with fine pink-tinged sand and clear water.
Durmitor National Park offers the best hiking and rafting in the country. The Tara Canyon — at 1300 metres deep, the deepest in Europe — is spectacular even from the road, and rafting the lower section takes you through the gorge properly. Žabljak, the nearest town, is a decent base. Snow usually covers the plateau into late spring.
Lake Skadar is the largest lake in the Balkans, shared between Montenegro and Albania. The Montenegrin side is a national park — you can rent a boat or kayak from Virpazar to visit floating meadows of water lilies and tiny island monasteries. Birdwatchers can tick 270 species.
Cetinje was the capital of Montenegro until 1918 and has a slightly melancholy beauty to it — grand embassies built for a tiny kingdom, a palace turned museum, and streets that feel genuinely untouched by tourism. Worth a half-day, especially combined with the coastal road from Budva.
Perast is an immaculate baroque village on Kotor Bay, with two small islands just offshore — Our Lady of the Rocks (man-made, with a church full of votive offerings) and a natural island with a monastery. A boat to the islands takes ten minutes. There's not a lot to do but it's one of the most pleasant places in the country to sit and have coffee.