Beginning in Kotor, my advice would be to obtain a map from the tourist information at the Venetian built Sea Gate but then put it away, safe in the knowledge you do have some help if you get horribly lost in the Stari Grad (Old Town). In other words, Kotor is a place to wander around with no set plan or destination in mind. At some point you will pass by the Maritime Museum, St Tryphon’s Cathedral, The Clock Tower, a stone pyramid and the Cats Museum, though not necessarily in that order. There will be time to admire the shops, squares, and churches of the Stari Grad and eat or drink coffee/beer in some of the numerous cafes and restaurants.
The more energetic can climb the 1350 steps to the fortress, situated 260 metres above the town, for unforgettable views of the Bay of Kotor and the old town with its seemingly triangular shaped walls. There may be a cruise ship docked at the quay while other, smaller boats will be ferrying visitors to some of the other sights in the bay, such as Perast and the Our-Lady-of-the-Rock Island. This is a view to savour and, in my opinion, it is better even than the view from Mount Srd over Dubrovnik as the grey, steep-sided mountains appear to clutch the bay in their grasp as they disappear to the horizon.