Kotor rewards the early riser. Start before the cruise crowds with the climb to the Fortress of San Giovanni — 1,350 steps switchbacking up the mountainside to the classic view over the fjord-like bay. Go at first light, carry water, and you'll have the ramparts almost to yourself.
Spend the rest of day one inside the Venetian walls: the maze of stone lanes, St. Tryphon's Cathedral, the maritime museum, and a long lunch of fresh Adriatic fish. As the afternoon cools, drive (or boat) the short distance to Perast — a single baroque waterfront facing the two island churches of Our Lady of the Rocks. Take the little boat out, then stay for a sunset dinner by the water.
Day two belongs to the bay itself. A morning kayak or small-boat cruise gets you into the quiet corners — the sunken submarine tunnels, the Blue Cave, hidden swimming coves. Back on land, wind up the Lovćen serpentine for pršut and cheese in the mountain village of Njeguši before the drive home.