If you make one trip out of Budva, make it Kotor. The city sits at the innermost point of the Bay of Kotor, where the mountains drop straight into the water, and it has been a UNESCO World Heritage Site since 1979. Its walled Old Town is bigger, more layered and, frankly, better preserved than Budva’s: medieval churches, Venetian palaces, and a maze of stone-paved lanes that reward getting lost.
The signature effort is the climb up the fortifications behind the town. The walls snake up the mountainside to San Giovanni Fortress, 260 m above the rooftops, and the view down over the terracotta Old Town and the fjord-like bay is the best in Montenegro that you can reach on foot. In summer do it early morning or near sunset, carry water, and expect a ticket in season.
Down in the town, St Tryphon Cathedral and the Maritime Museum anchor the sightseeing, but half the charm is unstructured: squares that open without warning, laundry strung between palazzi, and the famous cats of Kotor sunning themselves on every warm stone.
Getting there from Budva is easy: 28 km by road, about 40-50 minutes by car, or frequent buses that take around an hour. One warning shapes the whole day: Kotor is a major cruise port, so check the ship schedule mentality applies. Arrive before mid-morning or after the ships leave and you get a different, far better town.