While little remains of the 12th century castle (which was destroyed in 1706 at the behest of King Louis XIV), the hill offers spectacular views of the coast, the Baie des Anges, the Old Town, and the port. The very first image I saw of Nice, upon discovering which académie I had been placed in, was a shot of the coast taken from la Colline du Chateau. You have probably seen several versions of this image as well. Everyone who visits Nice has taken one, and for good reason! I knew I needed to take one of my own so one Saturday in early October I set off to climb the hill.
There is an elevator that will take you up to the top of the park, but if you can make the hike it is definitely worth the fairly minimal effort. There are several areas to stop and rest if necessary, as well as a few cafés along the way.
The park also boasts a waterfall and a cemetery. I recommend making the trip on a clear, sunny day in order to experience the best views. Entrance to the park is free though so you can go back as many times as you like without feeling like you have only one chance to make it perfect.