What was heaven called in greek mythology?

Answer 1

Elysium

Elysium was the island for a chosen few. The gods permitted only heroes or very good people to enter into this area.

Asphodel Fields

The Asphodel Fields were for the spirits of the common Greek. The majority of the population would be directed to here after death. Those who went to the Asphodel Fields were people who were neither particularly good or evil during their lives.

Tartarus

Tartarus was an area for those who were to be punished. In this place punishments were severe and unending. It was to Tartarus that Zeus sent the Titans after winning the battles against them. Mortals also could end up in Tartarus for crimes such as raping a daughter, hording wealth, committing fraud, and other more severe crimes.

A big answer, I know. but interesting, eh?