Climb the City Walls to San Giovanni Fortress
Hike the ~1,350 ancient stone steps that zig-zag up the mountainside to the fortress at roughly 1,200 ft, where the whole red-roofed UNESCO Old Town and the fjord-like bay open up beneath you. This is THE iconic Kotor image and the single thing first-timers most regret skipping. The trailhead is inside the walled town a few minutes from the ship, so it's fully independent of the cruise line; allow 1.5-2.5 hrs round trip and go early to beat the heat and crowds.