1) The origin of Naimiṣāraṇya: There seem to be two different origin stories revolving around the Naimiṣa forest. One etymology explains it as the ‘twinkling of the eye’, as Lord Viṣṇu destroyed the Asura army there, within the twinkling of the eye (nimiṣa). While the oher version explains the origin of the forest as the place where the wheel of righteousness (dharma-cakra) was shattered. It is told in the Vāyu-purāṇa:
1.1.165. “This wheel has a fine nave, its form and name are divine; it has truth for its spokes; its revolution is auspicious, and it is incomparable. You follow it alertly but with self-restraint as it proceeds ahead. You will then attain what is wholesome for you.”
1.2.7 The sages performed the sacrifice for a thousand years in the place where the rim of the revolving Dharma-cakra (the wheel of righteousness) was shattered. Thanks to that event, that place, sanctified by the sages, became famous as Naimiṣa.
The Devī-bhāgava-purāṇa gives an interesting variation of this story, adding the note that Kali has no influence in this place. (This means the influences of the Kali age)
1.2.26-32. ...When we were afraid of the Kali age, Brahmā gave us a Manomaya Chakra (wheel) and I said to all of us :-- Follow this wheel, go after it and the spot where the felly of the wheel will become thin (so as to break) and will not roll further, that country is the holy place; Kali will never be able to enter there; you all better remain there until the Satya age comes back. Thus, acording to the saying of Brahmā, we have got orders to stay here. On hearing the words of Brahmā, wo went out quickly keeping the wheel go on, our object being to determine which place is best and holiest. When we came here, the felly of the wheel become thin and shorn before my eyes; hence this Kṣettra is called Naimisa; it is the most sanctifying place.
Kali cannot enter here; hence the Mahatmas, Munis and Siddhas, terrified by the Kali age, have followed me and resorted to this place....
2) Māhātmya of Naimiṣāraṇya: According to Horace Hayman Wilson there should be a copy of the Naimiṣāraṇya-māhātmya in the original manuscript of the Vāyu-purāṇa:
It appears, however, that we have not yet a copy of the entire Vāyu Purāṇa. The extent of it, as mentioned above, should be twenty-four thousand verses. The Guicowar MS. has but twelve thousand, and is denominated the Pūrvārddha, or first portion. My copy is of the like extent. The index also spews that several subjects remain untold; as, subsequently to the description of the sphere of Śiva, and the periodical dissolution of the world, the work is said to contain an account of a succeeding creation, and of various events that occurred in it, as the birth of several celebrated Ṛṣis, including that of Vyāsa, and a description of his distribution of the Vedas; an account of the enmity between Vaśiṣṭha and Visvāmitra; and a Naimiṣāraṇya Māhātmya.
According to the Catalogue of the India Office Library, vol. 2, part i, p. 1688, it is contained in the Skanda-purāṇa. I have not been able to found it, however, the Skanda-purāṇa is the largest of all purāṇas so you might not want to rule its presence out.
Not exactly a Māhātmya, but a very short eulogy in praise of the Naimiṣāraṇya is found in the Brahma Purana:
1.1.4-12. In the very holy, charming and extremely sacred Naimiṣa forest, a great sacrifice lasting for twelve years was performed by the sages. The forest abounded in flowers of diverse kinds and trees such as Sāla, Karṇikāra, Panasa, Dhava, Khadira, Āmra, Jambū, Kapittha, Nyagrodha, Devadāru, Aśvattha, Pārijāta, Candana, Arjuna, Campaka and others. Many kinds of birds and beasts lived there. It abounded in Aguru, Pāṭala, Bakula, Sapta-Parṇa, Punnāga, Nāgakesara, Sāla, Tamāla, Nārikela and Arjuna. It was beautified by many trees, Campaka and others embellished by variety of water-reservoirds such as pools and holy lakes. It abounded in people of various castes—Brahmins, Kṣatriyas, Vaiśyas, Śūdras, people of all stages of life, students, householders, forest-dwellers and ascetics. It was richly endowed with birds of various sorts, cows and cattle wealth and storage of barley wheat, chick peas, pulses, beans, sesamum and sugarcan e and other plants. It was adorned by stocks of paddy and other fresh vegetables, There in that forest the bright sacred fire was kindled and the sages performed a sacrifice extending for twelve years. Thus the sages and other brahmins congregated there.
3) Gomatī River: There is an origin story of the Gomatī-kuṇḍa in the Skanda-purāṇa:
22.214.171.124-3. O holy Sir, earlier the eternal Gomatī Kuṇḍa was mentioned by you. At what time was it created? Kindly describe it in detail to us.
O highly intelligent one, listen to the story of the origin of Gomatīkuṇḍa. It is highly destructive of sins. It is a meritorious story formerly narrated by Rudra.
In the Naimiṣa forest, Śaunaka and other sages gathered together and held meritorious discussion regarding the splendid origin of all Tīrthas.
126.96.36.199-32. O holy Sir, Gomatī, the most excellent one among rivers, has come here itself. Perform here itself all your rites of Snāna, Dana etc. Gomatī has merged into the Yajña Kuṇḍa here. So did Sarasvatī.
Ever since then it is called Gomatī Kuṇḍa in the world. The path for all the worlds is here itself. Hence, O Vyāsa, this is highly meritorious and excellent Tīrtha on the earth. Thus Gomatī Kuṇḍa has been described. It is destructive of all sins.
On the eighth day in the dark half of the Bhādra month, Kṛṣṇa’s birth day (is celebrated). Devotees shall take holy dip there on that day and keep awake at night. After due observance of fast, O Vyāsa, they shall duly worship Vyāsa with his disciples(?)
4-5) Different places and tīrthas in and around Naimiṣāraṇya:
I have found an interesting story on the Siddhāśrama located with Naimiṣāraṇya, occuring in the Narada Purana:
1.1.24-27. Thereafter, those sages went to the holy Siddhāśrama in the forest. It abounded in groups of deer. It was graced with the residence of sages (living therein).
It was beautified with charming trees and creepers (full of abundant) flowers and fruits, and was spotted with lakes of crystalline water and was inhabited by persons warmly hospitable to guests (and strangers arriving there).
They (the sages of the Naimiṣa forest) saw the son of Romaharṣaṇa worshipping the infinite unvanquished Lord Nārāyaṇa, by means of the Agniṣṭoma sacrifice.
Suitably honoured by Sūta, those sages of well-known powers, remained there in the hall of sacrifice, awaiting the concluding rites of ablution (Avabhṛtha).