Everyone visits Athens and gets up to Acropolis hill to see the Parthenon and the city. Then he/she goes to Acropolis museum nearby and enjoys Acropolis from the same height. Never forget that it is a hill, and the hills around the city offer magnificent sight as well, especially Lycabettus.
View of Acropolis is the third top attraction in Athens. Here is a list that combines all sides of the city.
Moreover there are some options located at the rest of Athens hills, such as the restaurant at the top of Lycabettus hill. For top food options you can click here. Also there are open air cinemas that some of them offer a nice view to Acropolis as well.