Is purgatory a real place?
Purgatory birthed the thought that we will have a final chance to be saved after death. However, there is no Biblical indication of a purgatory or that there's a chance that God would let you be saved after death. So, no, after death there is not a final chance to be saved, and purgatory is not a real place.
Where is the place of purgatory?
According to Jacques Le Goff, the conception of purgatory as a physical place came into existence in Western Europe towards the end of the twelfth century. Le Goff states that the conception involves the idea of a purgatorial fire, which he suggests "is expiatory and purifying not punitive like hell fire".