I wouldn't classify Alanya as a cultural place but there are definitely good restaurants.
A visit to the Alanya castle is nice (drive up) and walk down is beautiful.
Alanya has a small archeological museum and an Ataturk museum. Neither are not very impressive.
Dimcay is worth a visit. There are several restaurants along an ice cold river.
There aren't a lot of English tourists in Alanya.
Many Scandinavians and Dutch in the small hotels/aparts near the centre of Alanya.
Lots of Germans and also Russians in the big All Inclusive 5 star hotels outside Alanya (Konakli, Avsallar, Incekum, etc).
Alanya has two main beaches: Cleopatra Beach and the East beach.
They are divided by the promontory.
Cleopatra Beach is wide and spacious. Sea gets deep rather quickly and there can be high waves (especially in October).
East Beach is not as wide but entering the sea is easier because it's more gradual and waves are less because of the peninsula.