The Castle Hill is the original site of Nice, which was once a walled medieval city on top of the hill dating back to the Celtic Ligurians. Hence the name, there was a castle in those earlier times but it was demolished in 1706. Now the site has turned into a park, and there are many view points of the city below. What you’ll find up top of the hill is a waterfall, ruins of a cathedral, and a cemetery that dates back to the late 1700s.
The panorama view of the city is a picturesque sight when you hike up, and I think it’s worth climbing up rather than taking the elevator as you won’t see the view. So, I’d definitely recommend taking the stairs!