pasparśa pādayor enaṁ
The specific “solitary place” where Indra approached Śrī Kṛṣṇa is mentioned by the sage Śrī Vaiśampāyana in the Hari-vaṁśa (Viṣṇu-parva 19.3): sa dadarśopaviṣṭaṁ vai govardhana-śilā-tale. “He saw Him [Kṛṣṇa] sitting at the base of Govardhana Hill.”
From the commentaries of the ācāryas we understand that Lord Kṛṣṇa wanted to provide a solitary meeting for Indra so that he would not be further humiliated. Indra came to surrender and beg forgiveness, and the Lord allowed him to do so privately.