Which are the exact lokas inhabited by the Apsaras according to different sampradayas?
Edit: Which lokas are the ones where Apsaras are born in the first place?
Apsaras are originally residents of a sub Loka named Apsara Loka, of the bigger Bhuvarloka. (Refer: How many lokas are there?)
The region above the earth and below the sun, known as Bhuvarloka is inhabited by many different kind of celestial races like Siddhas, Gandharvas, etc. This region is described as:
The region that extends from the earth to the sun, in which the Siddhas, etc (and other celestial beings) move, is called Bhuvarloka, which also I have described
-Vishnu Purāṇa 2.7.17
A story of the ascent of a Brahmin named Sivasarman through higher lokas is found in the Skanda Purāṇa where his journey after death is described fairly in detail. As per this, while the attendants of Bhagwan Vishnu were taking the Brahmin from earth, through all the lokas, soon after Gandharva Loka, they encountered Apsara Loka before they reached the sun.
Hearing the origin of the Apsarāloka, in this manner the eminent Brāhmaṇa reached the Solar World in a moment, travelling in an aerial chariot.
-Verse 28, Chapter 9, Kāśī khaṇḍa Pūrvārdha
This shows us that the Apasaras are one of the categories of celestials (as mentioned in the Vishnu Purāṇa) who live between the region above the earth and below the sun known as Bhuvarloka and near Gandharva Loka, have their own sub-loka allotted to them by the name of Apsara Loka.
Thus to sum up, Apsaras originally live in Apsara Loka of Bhuvarloka, between the earth and sun.
Often we come across a description where we see them frequenting other lokas or performing duties in other lokas as follows:
However as stated above their original Loka is the Apsara Loka where as per the very same chapter of the Skanda Purāṇa about 60,000 apsaras live. (Verse 12)
In fact as one can see though the incident of Apsara Urvashi and Arjuna in Swarga Loka finds mention in Mahabharata, verse 7 of this chapter of the Skanda Purāṇa mentions her as one of the residents of Apsara Loka, the original abode of the Apsaras.
Such a difference must be understood by the fact that Apsaras are originally the inhabitants of Bhuvarloka, however they do frequent other lokas. This is similar to when say an Indian goes abroad for work, holidaying, he is not called a resident of that country or even if he permanently moves there, his Indian relatives back home do not become residents of that Loka or multiple lokas (just by few Apsras moving about, other Apsaras don’t become residents of Swarga, Manidvipa, Kailasa) . His origin lies in India and he will be called an Indian only. In the same way Apsaras going for work (to serve in Indra’s Loka) will still be Apsaras (Indians) only and their origin will lie in Apsara Loka (India).
(Kausitaki Upanishad 1.3) : He going by the path by which the immortal gods travel reaches the world of Agni (fire), then to the world of Vayu (air), then to the world of Varuna, then to the world of Aditya (sun), then to the world of Indra, then to the world of Prajapati, then to the world of Brahma. In this world of Brahma, verily, is the lake Ara, points of time called Yestiha, the river Viraja, the tree Ilya, the city Salajya, the court of Aparajita, the door keepers Indra and Prajapati, the hall Vibhu, the throne Vicaksana, the couch Amitaujas, the beloved Manasi and her twin Caksusi weaving the worlds with flowers, Ambas (mothers), Ambavayis (nurses), Apsaras (celestial beauties), and the rivers called Ambayas. To this world comes the knower of this. To him Brahma says, "Welcome, you have my glory and you have reached the ageless river Viraja and you will never age."
Based on this verse from Kausitaki Upanishad we can say that Apsaras lived in Brahma-loka.