Google maps says that the Underworld is located in Sudan, Africa. Or at least the portal to it. 

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Hades is one of the very few gods that doesn't live on Mt. Olympus. He and his brothers (Zeus and Poseidon) make up the three biggest gods in Greek Mythology. After over-throwing Kronos, the brothers pick parts of the world to rule over. Hades, being the last to pick, got the part nobody wanted: The Underworld. He now spends his time watching over all the lost souls that wander in a purgatory-like afterlife and playing with Cerberus the guard dog. Many people today see Hades as solely the king of the underworld, but he is also has the power to control the precious metals of the earth. According to Rick Riordan, (author of the Percy Jackson and Lost Hero series) the children of Hades and a mortal are either given the power to raise an undead army or gravitate objects like gold and silver towards them. The Greeks worshipped their ghastly death god in hopes for a good resting place. Resting place meaning they would wish that they wouldn't be stuck the torturous one for all eternity. There were three different areas: The paradise afterlife, the torturous afterlife (as previously mentioned), and the mediocre afterlife. The last one was not somewhere you wanted to be. It was the type of place where you would eventually forget who you were, how you died, and aimlessly wander in a colorless, eternal wheat field. There was no day or night, no sun or rain. You were stuck as a lifeless soul in a lifeless place. Now you can see why Hades hates this place.