[PADA: Thanks to Yasodananda das for these quotes]
Srila Prabhupada explains the history of the discovery of Radha-Kunda:
The spot where we now find Śrī Rādhā-kuṇḍa was an agricultural field during the time of Caitanya Mahāprabhu. A small reservoir of water was there, and Śrī Caitanya Mahāprabhu bathed in that water and pointed out that originally Rādhā-kuṇḍa existed in that location. Following His directions, Śrīla Rūpa Gosvāmī and Sanātana Gosvāmī renovated Rādhā-kuṇḍa.
This is one of the brilliant examples of how the Gosvāmīs excavated lost places of pilgrimage. Similarly, it is through the endeavor of the Gosvāmīs that all the important temples at Vṛndāvana were established. Originally there were seven important Gauḍīya Vaiṣṇava temples established in Vṛndāvana, namely, the Madana-mohana temple, Govinda temple, Gopīnātha temple, Śrī Rādhāramaṇa temple, Rādhā-Śyāmasundara temple, Rādhā-Dāmodara temple and Gokulānanda temple.
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Adi-lila : Adi 10: The Trunk, Branches and Subbranches of the Caitanya Tree : Adi 10.90
Distinguishing between pure devotees and internal or confidential devotees, Śrī Rūpa Gosvāmī, in his book Upadeśāmṛta, traces the following gradual process of development. Out of many thousands of karmīs, one is better when he is situated in perfect Vedic knowledge. Out of many such learned scholars and philosophers, one who is actually liberated from material bondage is better, and out of many such persons who are actually liberated, one who is a devotee of the Supreme Personality of Godhead is considered to be the best. Among the many such transcendental lovers of the Supreme Personality of Godhead, the gopīs are the best, and among the gopīs Śrīmatī Rādhikā is the best. Śrīmatī Rādhikā is very dear to Lord Kṛṣṇa, and similarly Her ponds, namely, Śyāma-kuṇḍa and Rādhā-kuṇḍa, are also very dear to the Supreme Personality of Godhead.
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Adi-lila : Adi 7: Lord Caitanya in Five Features : Adi 7.18-19
Āriṭ-grāma is also called Ariṣṭa-grāma. Śrī Caitanya Mahāprabhu understood that in that village, Ariṣṭāsura was killed by Śrī Kṛṣṇa. While there, He inquired about Rādhā-kuṇḍa, but no one could tell Him where it was. The brāhmaṇa accompanying Him could also not ascertain its whereabouts. Śrī Caitanya Mahāprabhu could then understand that the holy places known as Rādhā-kuṇḍa and Śyāma-kuṇḍa were at that time lost to everyone's vision. He therefore discovered Rādhā-kuṇḍa and Śyāma-kuṇḍa, which were two reservoirs of water in two paddy fields. Although there was very little water, Śrī Caitanya Mahāprabhu was omniscient and could understand that formerly these two ponds were called Śrī Rādhā-kuṇḍa and Śyāma-kuṇḍa. In this way Rādhā-kuṇḍa and Śyāma-kuṇḍa were discovered.
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Madhya-lila : Madhya 18: Lord Sri Caitanya Mahaprabhu's Visit to Sri Vrndavana : Madhya 18.3 : PURPORT
"Of all the gopīs, Rādhārāṇī is the dearmost. Similarly, the lake known as Rādhā-kuṇḍa is very dear to the Lord because it is very dear to Śrīmatī Rādhārāṇī
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Madhya-lila : Madhya 18: Lord Sri Caitanya Mahaprabhu's Visit to Sri Vrndavana : Madhya 18.7 : TRANSLATION :
"The attraction of Rādhā-kuṇḍa is as sweet as that of Śrīmatī Rādhārāṇī. Similarly, the glories of the kuṇḍa [lake] are as glorious as Śrīmatī Rādhārāṇī.
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Madhya-lila : Madhya 18: Lord Sri Caitanya Mahaprabhu's Visit to Sri Vrndavana : Madhya 18.11 : TRANSLATION :
"Because of its wonderful transcendental qualities, Rādhā-kuṇḍa is as dear to Kṛṣṇa as Śrīmatī Rādhārāṇī. It was in that lake that the all-opulent Lord Śrī Kṛṣṇa performed His pastimes with Śrīmatī Rādhārāṇī with great pleasure and transcendental bliss. Whoever bathes just once in Rādhā-kuṇḍa attains Śrīmatī Rādhārāṇī's loving attraction for Śrī Kṛṣṇa. Who within this world can describe the glories and sweetness of Śrī Rādhā-kuṇḍa?"
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Madhya-lila : Madhya 18: Lord Sri Caitanya Mahaprabhu's Visit to Sri Vrndavana : Madhya 18.12 : TRANSLATION
"Śrī Caitanya Mahāprabhu then marked His body with tilaka made from the mud of Rādhā-kuṇḍa, and with the help of Balabhadra Bhaṭṭācārya, He collected some of the mud and took it with Him"
Books : Sri Caitanya-caritamrta - 1975 Edition : Cc. Madhya-lila : Madhya 18: Lord Sri Caitanya Mahaprabhu's Visit to Sri Vrndavana : Madhya 18.14 : TRANSLATION
Lectures : Srimad-Bhagavatam Lectures : Canto 1: Lectures : SB 1.1: Lectures : Srimad-Bhagavatam 1.1.9 -- Auckland, February 20, 1973 : 730220sb.auc :
Prabhupāda: Yes. The ācārya or gosvāmī, their business is... Just like our ācāryas, sad-gosvāmī, they left their service, big service, ministership, and by the order of Caitanya Mahāprabhu they went to Vṛndāvana. But what for, going to Vṛndāvana and sleeping and eating? No, no, not for that purpose. They, rather at home they had time to sleep more, but when they went to Vṛndāvana they were sleeping only one half-hour to two hours only. At the present moment when a man becomes old, he requires more rest. But according to Vedic civilization, no more rest, more work, more work. But these gosvāmīs, they were deputed by Lord Caitanya Mahāprabhu... At that time this Vṛndāvana, which you have seen, now it is nice city, but during the time of Caitanya Mahāprabhu it was a big field only, that's all, nothing was there. Everything, all Kṛṣṇa's līlā were vanished. Not vanished, it was not visible. Caitanya Mahāprabhu saw one small hole, little water, and He indicated, "This is Rādhā-kuṇḍa."
Then Rādhā-kuṇḍa was discovered. So these Gosvāmīs were working very hard. And special business was there, nana-śāstra-vicaraṇaika-nipunau. They were very expert in scrutinizingly studying all the Vedic literatures. Nana-śāstra, śāstra, not ordinary knowledge. They were also reading(?). Nana-śāstra-vicaraṇaika-nipunau. Just like Rūpa Gosvāmī has quoted so many verses, so many incidences from different śāstras, how the biography is stated there in compiling Bhakti-rasāmṛta-sindhu, which we've translated, Nectar of Devotion. So this Nectar of Devotion, because formerly whatever is given under Vedic evidence it will be accepted always correct. Therefore nana-śāstra-vicaraṇaika. They used to collect all the Vedic references and put into Bhakti-rasāmṛta-sindhu to establish that bhagavad-bhakti, devotional service to the Lord, is the ultimate goal of life. Nānā-śāstra-vicāraṇaika-nipuṇau sad-dharma-saṁsthāpakau. Sad-dharma. Not asad-dharma. Asad-dharma means referring to the body, karma-kāṇḍīya. Karmīs they are engaged in asad-dharma not sad-dharma. Because the body is asat. antavanta ime dehā nityasyoktāḥ śarīriṇaḥ [Bg. 2.18].