In Bhakti Ratnakar it is mentioned that the place of appearance of Srimati Radharani is Sri Raval Dham.

anayārādhito nūnaṁ
bhagavān harir īśvaraḥ
yan no vihāya govindaḥ
prīto yām anayad rahaḥ
(Srimad Bhagavatam 10.30.28)

Srila Bhaktivinoda Thakur’s translation: O gopi, certainly She, for whom Sri Krishna had left all of us and took Her alone to a secluded place, is a better servitor of Supreme Lord Sri Hari. The inherent purport is that since She is the crest jewel among the other female consorts of Sri Krishna, Her name is Sri Radhika.

In the Brihad-Gautamiya-Tantra the name of Sri Radharani is vividly explained –

devī kṛṣṇa-mayī proktā
rādhikā para-devatā
sarva-lakṣmī-mayī sarva-
kāntiḥ sammohinī parā
(Chaitanya Charitamrita Adi 4.83)

Apart from these, the actual identity and glories of Sri Radhika are narrated in great detail in Sri Chaitanya Charitamrita by Srila Krishnadas Kaviraj Goswami, in Govinda-lilamrita and scriptures compiled by the Goswamis.

A brief description about Sri Radharani from Sri Brahmavaivarta Purana is as under:

In the arena of highest divine mellow in the abode of Goloka She, who appeared from the left hand side of Sri Krishna and got attracted and ran towards Him, is known as ‘Radha’. Radha appeared from Sri Krishna and is His non-different manifestation. Hence She is dear-most to Sri Krishna. From the sweat pores of Sri Radharani million crores of cowherd girls and from the sweat pores of Sri Krishna, million crores of cowherd boys and cows appeared.

One time when Sri Krishna was engaged in pastimes with Sri Viraja, the messengers of Srimati Radharani went to Her and complained Her about this. Sri Radhika in an angry mood rushed towards Sri Krishna. Seeing this, Sudama, the associate of Sri Krishna, informed Him about the arrival of Srimati Radhika. Thinking that Radharani’s arrival at that place would turn the situation troublesome, Sri Krishna along with Sudama and other friends ran away from there. Viraja gave up her body and became a river. After reaching the place Radharani could not find anyone. Later when Sri Krishna met the eight principle gopis and Radharani, She chastised Him severely. When Sudama could not tolerate this and objected Her, She cursed him that he would take birth as a demon. Sudama also cursed Her in return, “You will take birth in earthly planet falling from Goloka having to tolerate the intolerable separation from Sri Krishna.” Sudama became Shankachuda demon being cursed by Radharani.

The essence of the narration about the appearance of Sri Radharani as explained in Sri Radha Tantra is the following:

Lord Vasudeva once worshipped Yogamaya for a long duration when Yogamaya appeared and said, “You cannot attain perfection by performing the penance alone without being accompanied by Lakshmi Devi. The four garlands around my neck – Hastini, Padmini, Chitrini and Gandhini are my messengers. The Padmini garland will be known as Radha in the abode of Vraja. Go to Vraja and meet Padmini. By this Your penances will be successful.” After listening to the words of Yogamaya, Lord Vasudeva desired to see the form of Padmini. Immediately goddess Padmini appeared in front of Lord Vasudeva in an effulgent and reddish thousand petal lotus flower. Lord Vasudeva was surprised by beholding the form of Padmini. She (Padmini) only performed the pastime of appearing in the form of an egg in a Lotus flower in the river Kalindi.

King Vrishabhanu was engaged in the worship of Yogamaya on the banks of river Kalindi in order to get a beautiful baby. Yogamaya Katyayini, being satisfied by his worship, gave the aforementioned effulgent egg to king Vrishabhanu and said, “I am subdued by your wife’s devotion; give this egg to her. You will be blessed with a beautiful baby girl. As soon as Vrishabhanu placed the egg in front of his wife Kirtida, the egg broke and Sri Radharani appeared.

Regarding the appearance of Sri Radharani it is also said – by the fruit of the penances of king Vrishabhanu on the banks of river Yamuna, Radharani self-manifested on an unprecedented hundred petal lotus flower in Yamuna. Vrishbhanu was extremely pleased being blessed with a wonderful and most beautiful baby girl but saw that the eyes of the baby were closed. He was all the while unhappy internally for the baby being sightless. One day his friend king Nanda along with his wife Yasodadevi and the child Gopal came to his place. While Vrishabhanu was narrating his sorrow to king Nanda one surprising incident took place. Small Gopal crawled towards Radharani and touched Her. She immediately opened Her eyes. Radharani had taken a vow that she would see Krishna only when She opens Her eyes for the first time. Hence as soon as Krishna came She opened Her eyes.