TheSkull Keyis used to unlock theSkull Cavern. The Skull Cavern resides in a cave in the top-left hand corner of theCalico Desert, accessed by the bus. The Skull key is found if you reach the 120th level of the mine which is also the bottom of the mine.
When you get the Skull Key, you can play theJunimo Kartarcade machine inThe Saloon. It is located in the far right room next to theJourney of the Prairie Kingarcade machine. The reward for beating theProgress Modeof the game is a copy of the game in a console version. This copy can be placed at the farm's house.
You can find the Skull Key in your 'Wallet' in theThe Player's Menu within the Skills tab.