A great place to relax in the sun or in the shade with great views over the water and the Lower town. You can take the funicular from here (right near the statue, located in the glass house) to reach the Lower town, or you can wall all the way to the Citadel (the entrance is on the opposite site though, if you want to visit it). Lots of information about the origins of the terrace and several musicians to entertain you.
A very romantic place, if you like history and it reminds me of so many historic European cities.
To one side, there are several hotels, some older than others, with probably bird eye view over this whole location.