The Wikipedia article suggests that Sita was either from Bihar or Nepal:
Born: Either present-day Sitamarhi district, Bihar, India or Janakpur, present-day Nepal (both the places were part of the Mithila Kingdom)
Another non-verified article suggests that she was from Nepal.
During her second exile, she was sheltered in hermitage of Valmiki. Which geo location did that place belong to?
Sita was daughter of King Janak, the ruler of the Kingdom of Videhas/Mithila.
In the Ramayana, Sita is the princess from Videha, who marries Rama creating an alliance between the kingdoms of Kosala and Videha. The capital of Videha is believed to be either Janakpur (in present-day Nepal), or Baliraajgadh (in present-day Madhubani district, Bihar, India). During the late Vedic period (c. 900 – c. 500 BCE), Videha became one of the major political and cultural centers of South Asia, along with Kuru and Pañcāla. Late Vedic literature such as the Brahmanas and the Brihadaranyaka Upanishad both mention Janaka, as a great philosopher-king of Videha, renowned for his patronage of Vedic culture and philosophy, and whose court was an intellectual centre for Rishi (sages) such as Yajnavalkya
Videha kingdom is also called Mithila. Nimi is considered to be the first king of the Videha kingdom and belonged to the Janaka lineage of Mithila. Nimi was the grandson of Manu and son of Ikshwaku. Maithali language of Mithila kingdom is still spoken today in the regions of Bihar and Nepal.
The native language in Mithila is Maithili, and its speakers are referred to as Maithils. The name Mithila is commonly used to refer to the Videha Kingdom, as well as to the modern-day territories that fall within the ancient boundaries of Videha. In the 18th century, when Mithila was still ruled in part by the Raj Darbhanga, the British Raj annexed the region without recognizing it as a princely state. Mithila comprises Tirhut, Darbhanga, Kosi, Purnia, Munger, Bhagalpur and Santhal Pargana divisions of India and some adjoining districts of Nepal.
So, there was a Janak lineage of kings of Mithila. All the kings of Mithila including first king Nimi were called Janak as the word Janak means father and the king is a father of his kingdom metaphorically. There had been many king Janaks, one was father of Sita during Treta Yug and another was teacher of Shukadeva, son of Vyasa during Dwapra Yug and another Janak was disciple of Ashtavakra and to whom Ashtavakra Geeta was discoursed. Other king Janaks and their courtyard discussions are mentioned in Vedas.
During her exile, Sita stayed in the Valmiki Ashram which is called Bhagwan Valmiki Ramtirth Sthal today.
Bhagwan Valmiki Tirath Sthal, dedicated to Maharishi Valmiki ji is situated 11 km west of Amritsar on Amritsar Lopoke road. As per the mythological beliefs, The temple dates back to the period of Ramayana and the place is famous for the ashram of sage Maharishi Valmiki. It is the place where the sage gave shelter to Sita, wife of Rama when she was abandoned after the Lanka Victory. The place is birthplace of Lava and Kusha, sons of Ramachandra, in ashrama of Saint Balmiki. The great epic Ramayana is also said to have been written here by Maharishi Valmiki. It is also believed that the fight between Lord Ram Chandra's forces and Lav and Kush had also taken place at Ram Tirth.
It is also known that Lav and Kusha founded the cities of Lahore and Kasur(now Amritsar).
For the exact location of Sita, we need to trace the path of Rishi Vishwamitra, God Rama and Lakshmana after they left Ayodhya.
Vishwamitra taught God Rama bala and atibala mantra, at present-day Shringi ashrama near Sherva ghat in Uttar Pradesh state. Then they reached the spot where Kamadeva was burnt by God Shiva, present-day Kameshwar Dham near Ballia [Valmiki Ramayana 1.22-23].
God Rama killed Tadaka and they reached Siddhashrama, at present-day Charitra-vana near Buksar in Bihar. Nearby, He flung Mareecha and Subahu was killed [Valmiki Ramayana 1.26-30].
They rested on the banks of River Son, then crossed River Ganga and reached the city of Vishala, present-day Vaishali in Bihar [Valmiki Ramayana 1.31, 1.45].
They reached (the kingdom of) Mithila where God Rama redeemed Ahalya, present-day Ahalya uddhara sthana in Ahiyari South in Bihar [Valmiki Ramayana 1.48].
They went north-east and reached (the capital city of) Mithila where King Janaka was performing a yagnya and hundreds of tents were set up [Valmiki Ramayana 1.50]. Janaka said he had found Sita in the ground, present-day Sitamarhi in Bihar.
Ministers then entered the city and got God Shiva's celestial bow on a 8-wheeled cart pulled by 5,000 strong men. God Rama strung the bow [Valmiki Ramayana 1.67-68]. It is believed to be at present-day Rangbhoomi ground in Janakpur in Nepal, and that a piece fell far away at Dhanushdham near Janakpur.
Envoys travelled to convey the message to the royals at Ayodhya spending 3 nights on the way. The convoy took 4 days to reach Mithila, after which God Rama married Sita [Valmiki Ramayana 1.68-69]. This is believed to be at present-day Janakpur in Nepal.
Much later, Lakshmana took a pregnant Sita in a chariot from Ayodhya up to the banks of River Ganga. They then took a boat to cross over to reach the ashrama where Valmiki and many ascetic families lived [Ramayana 7.56-59]. This is present-day Bithoor near Kanpur, where she delivered her twins.
There are other Valmiki ashrama too, identified in present-day Amritsar in Punjab state; Valmikinagar on the Bihar state border with Nepal; Tapovan Hill near Vaidyanath jyotir-linga temple in Deoghar in Jharkhand state; and Thiruvanmiyur in Chennai in Tamil Nadu state.
Sources: Bihar Tourism website; ramyatra.com; templepurohit.com; 'Essence of the Fifth Veda' by Gaurang Damani pgs 4, 5, 6, 62.
According to Bala Kanda, after elimination of Subahu and sparing the life of Mareecha by throwing him into Ocean, Sri Rama along with Sage Viswamitra reached the Northern Banks of Ganga and from there he reached the city of Vishala. Thereafter, they reached Mithila, the city of Janaka.
इति उक्त्वा मुनिशार्दूलः कौशिकः स तपोधनः | उत्तराम् दिशम् उद्दिश्य प्रस्थातुम् उपचक्रमे || १-३१-१६
Thus saying farewell to woodland-deities that descendent of Kaushika, namely Vishvamitra, the saint whose wealth is his ascesis started to journey on aiming to reach the northern side of River Ganga.
Sage Valmiki did not narrate explicitly the distances travelled by them for reaching Mithila (at least in Yojanas).
We don't know whether the geographical locations, names of towns of that era remained the same even now also.
Some believe that Nashik is the place, where Surpanakha was disfigured, and some others feel it is near Bhadrachalam, Telangana.
Similarly, the case with the city of Janaka, Mithila, the birth place ofor Sita. Everyone according to one's perception.
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2nd part of the question where did Sita stay during pregnancy?
Sita's pregnancy was mentioned in Uttar Kanda.
It is to be remembered that Uttar Kanda is an interpolated story.
Ramayana ends with coronation of Sri Rama as the king of Kosala Kingdom.
