Elio had especially chosen that place to carry out his plan. Because that was the perfect place to draw Andrew to him. Because that was the perfect place to make him fall into his trap.
But that wasn't the only reason Elio had chosen that place. There were many other deep reasons.
First, because he had planned to take him to see the place from the beginning, knowing he would love that. He wanted to make his wild kitten happy.
Second, because that place was his peace, and Andrew had become his peace too. So he wanted to take his peace to his peaceful place. He wanted to share his most important place with him.
Third, to make Andrew see all parts of him, his everything, and make him realize how much he meant to him by revealing his hidden place.