From the top of the Kotor fortress, you get an absolutely stunning view of the area. The red-roofed houses right below are Kotor's Old Town historic district, though the town itself sprawls on both sides of the bay.
The steps at the bottom look innocent enough, but remember you have 1,350+ of them to go (plus whatever you hiking you plan to do beyond the fortress walls).
Some sections will give you the option to deviate off the main steps and travel along smoother paths. While in the end you have to climb the same elevation, the fortress has three different routes of ascending difficulty to provide something for all.
Aside from the main cathedral at the base of the fortress, the tower of the Church of our Lady of Remedy is one of the most iconic sites along the fortress.
Be on the lookout for signage painted along the the fortress walls. They'll tell you (somewhat clearly) where major intersections between routes lie. Also, look out for red and white targets that mark the trails into the mountain regions.
Shortly after the Castle of San Giovanni, be on the lookout for a target marker painted next to a hole in the wall. Climb through it for access to all the hiking trails, as well as a short trek to a house that sells homemade cheese and rakija.
As seen form the fortress, the Restaurant Nevjesta Jadrana, which is located right at the top of the Ladder of Cattaro (the 70+ switchbacks you can see from the fortress). Its gray stones are hardly noticeable among the desolate landscape.