Nice has a hill, Castle Hill (or le Montée du Châteaux, or la Colline du Châteaux in French), between the city and the harbor, where one can climb and see the roman ruins of the original city. It is a beautiful walk (be ready, it is a workout), with a surrounding park, small cascade, and, once in the ruins, beautiful mosaics. The view of the city and Mediterranean below from that vantage point is spectacular.
Hope this helps you "tourist" the place yourself, like Richard did.
|Cascade on way to the ruined Roman city.|
|Original mosaics from the ruins.|
|Vantage point view of Nice and the Mediterranean.|