Getting to the highest point to explore the terrain is the right decision. You can immediately see the entire city and start orienting in it. Practical travelers will appreciate the compass map on Castle Hill. If topography is not your cup of tea and your soul is craving for beauty, you should go further up. Here you will find "that" view of the Promenade des Anglais on the one side and the snow-white yachts in the port of Nice on the other side.
Once upon a time, there really was a castle and a fortress on top of this hill, which protected the city from invaders. But its bastions did not withstand the 54-day assault during the siege of Nice in 1706, and all the structures were demolished to the ground. Thus, today archeology fans will only find ruins of an XI century cathedral here.
There is no need to climb the mountain on foot — to the left of the stairs, next to the Hotel Suisse, you will find a passage to the elevator. However, it does not work around the clock, so do not forget to check the schedule.