The determined citizens of Ayodhya followed God Rama, Sita and Lakshmana to the forest up to the banks of River Tamsa. They decide to leave before the crack of dawn, when the citizens are still asleep. They cross River Tamsa and then River Gomti [Ref: Valmiki Ramayana 2.45-49].
They reached the banks of River Ganga at Shringverapura, a region ruled by their friend Nishada King Guha. Then, they cross River Ganga in a sturdy boat having a rudder [Ref: Valmiki Ramayana 2.50-52], driven by boatman Kevat. This is present-day Shringverpur in Uttar Pradesh state.
They reach Rishi Bharadwaja’s ashrama at the confluence of River Ganga and Yamuna, present-day Prayagraj in Uttar Pradesh state. Bharadwaja advises them to go westwards and stay at an idyllic place called Chitrakoot. Accordingly, they cross River Yamuna and travel to Chitrakoot which is on the border of present-day states of Madhya Pradesh and Uttar Pradesh [Valmiki Ramayana 2.54-56].
Later, Bharata says he will rule in God Rama’s name from the outskirts in Nandigrama, present-day Nandagaon near Ayodhya [Ref: Valmiki Ramayana 2.112-115; Garuda Purana chapter 143]. Present-day Chitrakoot has caves with a Shiva-linga and big seats made of stone with intricate carvings, where God Rama stayed. Even today, one can visit locations in Chitrakoot like Rama ghat, Sita rasoi, Janaki kund and Bharat-milap temple.
From Chitrakoot, God Rama, Sita and Lakshmana visit the nearby ashrama of Rishi Atri and Anasuyadevi. The learned sage describes to God Rama that the wicked Rakshasas come from the nearby forest and prevent them from performing their Vedic rituals [Ref: Valmiki Ramayana 2.117-119]. God Rama goes into the forest and kills Viradha Rakshasa. They reach Rishi Sharbhanga's ashrama [Valmiki Ramayana 3.3-5].
There is a Sati Anasuya ashrama 16 km from present-day Chitrakoot, nearby are Viradh-kund and Sharbhanga ashrama [Ref: holydham.com].
From Rishi Sharabhanga's ashrama, travelling a long way in the Dandaka forest crossing many rivers to reach Rishi Suteekshna's ashrama. Then, they pass many mountain peaks, forests, streams and rivers and lived near various ascetics for 10 years and return to Rishi Suteekshna's ashrama. From here they visit Rishi Agastya nearby [Ref: Valmiki Ramayana 3.9-11].
A (truncated) Dandaka forest exists today in present-day southern Chhattisgarh state, bordering Telangana state. Many evidences of their presence are found in present-day Ramtek in Maharashtra, and Parnasala on the banks of River Godavari in Telangana state near the temple town of Bhadrachalam which is also called Dakshina Ayodhya. There is an Agastya ashrama on the banks of River Pravara at Aroli village in Akole taluka, south of Nashik. Another Agastya Rishi temple is on Ankai hill, east of Nashik.
Agastya guides them to the nearby Panchavati [Ref: Valmiki Ramayana 3.13]. This is believed to be present-day Nashik in Maharashtra state having locations like Panchvati, Tapovan, Rama-kunda, Sita-gufa and Lakshmana-kunda. God Rama, Sita and Lakshmana also worship Goddess Durga at the nearby Saptashrungi temple as per local folklore.
While Ravana is flying away in the pushpaka-vimana, Sita’s cries of help are heard by the bird Jatayu who fought against Ravana. There is a Jatayu hill-temple at present-day Uddhar near Pali in Maharashtra state, believed to be his residence. Sita drops her ornaments, especially when she sees 5 monkeys sitting on a hill near Kishkindha, present-day Hampi in Karnataka state. This is to leave a trail for God Rama to find her [Ref: Valmiki Ramayana 3.49-54].
It is believed that God Rama had met Jatayu at Lepakshi (meaning ‘rise bird’) village, 15 km east of present-day Hindpur in Anantapur district of Andhra Pradesh state.
The 2 brothers immediately set out in search of Sita.
As per local folklore, the extreme west location reached by the brothers is just off the sea-shore. Here, God Rama fires an arrow to obtain sweet water and worships God Shiva after making a Shiva-linga using walu (sand). Hence these places got named Banganga and Walkeshwar, in present-day Mumbai. Then they again move inland. They worship Goddess Bhavani at present-day Tuljapur in Maharashtra state.
Kavandha Rakshasa tells the 2 brothers to meet Sugreeva at Rishyamukha mountains on the banks of Pampa sarovar, which is on the outskirts of the kingdom of Kishkindha, present-day Hampi in Karnataka state [Ref: Valmiki Ramayana 3.72].
[Source: 'Essence of the Fifth Veda' by Gaurang Damani pages 9, 11, 12, 23-27].