Bathing in the Postiguet beach or simply walking along its shore in summer is quite an experience, thanks to being able to contemplate the beautiful castle of Santa Bárbara, full of history and Site of Cultural Interest.
Its reform and construction as we know it now dates back to 1580 but more than three centuries before, the future King Alfonso X "el Sabio" took the fortress from the Arabs in 1248 after stiff resistance.
But don't think that the beautiful views are only from the beach because those from the castle are even better, as you can see in the photograph below.
Without a doubt, Alicante, even though it's a small coastal city, has a lot of charm and a lot of history. If you have the opportunity to visit it, do it, and enjoy its charm and good food.
Source on which I relied to give some accurate info about the castle: (1)