Answer to this Question: Lord Rama's path to exile from Ayodhya in today's India describes the approximate path of Lord Rama's travel during the exile, but Nashik is not mentioned. According to the Wikipedia page of Nashik, it is the place where he cut the nose of Shurpanakha, therefore the name Nashik, also Panchavati is also located in Nashik, so did he visit Nashik? If yes then during which phase of his exile did he go there?
Many scholars/devotees of Sri Rama declared different route maps, depicting Sri Rama's journey during the exile period of 14 years.
a) The most popular one was pasted below.
b) In Southern India, it was strongly believed that Sri Rama spent 3 years, after roaming in Dandaka Forest for 10 years, near Parnasala at Bhadrachalam in Telangana State of India.
तत्र संवसतः तस्य मुनीनाम् आश्रमेषु वै || ४-११-२६ रमतः च आनुकूल्येन ययुः संवत्सरा दश |
While Raghava stayed comfortably taking delight in those hermitages of sages, indeed ten years have smoothly elapsed.
In the 14th year, after Sita's abduction, it was believed that Sri Rama and Lakshmana crossed River Godavari and finally reached Kishkinda (present day Karnataka).
So whether it was from Panchavati in Maharashtra State or Parnasala in Telangana State people believe that after Sita's abduction, it was believed that Sri Rama and Lakshmana crossed River Godavari and finally reached Kishkinda (present day Karnataka).
Sage Valmiki did not clearly mention as to the position of Sage Suteekshna in the Dandaka Forest. It was Sage Suteekshna, who gave directions to Sri Rama to Sage Agastya's hermitage.
योजनानि आश्रमात् तात याहि चत्वारि वै ततः | दक्षिणेन महान् श्रीमान् अगस्त्य भ्रातुर् आश्रमः || ४-११-३७
"On your going four yojana-s from this hermitage, oh, dear Rama, there is the great and glorious hermitage of Agastya's brother on the southern side."
दक्षिणाम् दिशम् आस्थाय वन षण्डस्य पार्श्वतः || ४-११-४० तत्र अगस्त्य आश्रम पदम् गत्वा योजनम् अन्तरम् |
"On going one yojana beyond, taking the southward course on the side of the forest clump you will find Agastya's hermitage."
Hence, Sri Rama travelled 5 yojanas ,i.e,, 65 Kms (13 x 5 ) in Southern direction for reaching Sage Agastya's hermitage.
Sage Agastya directed Sri Rama to dwell at Panchavati, which is nearer to his hermitage.
इतो द्वि योजने तात बहु मूल फल उदकः | देशो बहु मृगः श्रीमान् पंचवटि अभिविश्रुतः || ३-१३-१३
"A most prosperous place called Panchavati is there at a distance of two yojana-s from here, oh, dear Rama, which is abundant with tubers, fruits, water, and many deer." Thus Agastya started to tell.
So Panchavati was nearly at a distance of two yojana-s ,ie., 26 Kms from Sage Agastya's hermitage. Therefore, we cannot exactly fix the place of Panchavati, taking clues from Srimad Ramayana.
It can be anywhere along the course of river Godavari or its tributories, as we do not know whether people of that era used to call which river with which name!
After performing the last rites of the bird Jatayu, near Panchavati, Sri Rama travels nearly 3 Krosa or 11 Kms distance before reaching Krauncha Forest.
ततः परम् जनस्थानात् त्रि क्रोशम् गम्य राघवौ | क्रौंच अरण्यम् विविशतुः गहनम् तौ महौजसौ || ३-६९-५
Thereafter, both the highly vigorous Raghava-s have entered the impassable Kraunca forest, on going three krosa-s from Janasthaana.
ततः पूर्वेण तौ गत्वा त्रि क्रोसम् भ्रातरु तदा | क्रौंचारण्यम् अतिक्रम्य मातंग आश्रम अंतरा || ३-६९-८
Then, both the brothers on passing over that Kraunca forest and on going from there eastwardly on a three-krosha route, those sons of Dasharatha have seen a horrendous forest in between Kraunca forest and Matanga hermitage.
After having a fight with Kabandha, and upon his direction the 2 brothers reached Pampa and Kishkinda. So Kishkinda is not much far off from Panchavati.
Again when sending the troops to Southern direction in search of Sita, Sugriva orders them to start their search from Vindhya Mountains.
तेषाम् अग्रेसरम् चैव बृहद् बलम् अथ अंगदम् | विधाय हरि वीराणाम् आदिशद् दक्षिणाम् दिशम् || ४-४१-६
Sugreeva made the formidably mighty Angada as the chief of those valiant monkeys forming search party and ordered southern direction for them.
सहस्र शिरसम् विंध्यम् नाना द्रुम लता आयुतम् | नर्मदाम् च नदीम् रम्याम् महोरग निषेविताम् || ४-४१-८
"Search the thousand crested Vindhya mountains abounding with numerous tress and climbers, then the delightful Narmada river coursing a little southerly to that range, which is adored by great snakes”.
Now a question arises, if Kishkinda was in area of present day Karnataka state, why should Sugriva order vaanaras to start their search from Vindhya mountains and stated to cross Narmada river, which are located in Madhya Pradesh area?
Any sane person will decide the 4 directions, ie., North, South, East and West, according to his place of stay only, but not somewhere else.
Hence, Kishkinda might have have been located in the area of present day Madhya Pradesh or Chattisgarh only, but not Karnataka state, as commonly believed.
People of that era might be referring to Sabari river, a tributary to River Godavari, as Godavari and originates in Chattisgarh area and merges in river Godavari near Kunavaram, nearly 53 Kms away from Bhadrachalam of Telangana State.
From Ayodhya, God Rama, Sita and Lakshmana 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 which is on the border of present-day states of Madhya Pradesh and Uttar Pradesh [Valmiki Ramayana 2.54-56]. Even today, one can visit locations in Chitrakoot like Rama ghat, Sita rasoi, Janaki kund and Bharat-milap temple.
There is also Sati Anasuya ashrama 16 km from present-day Chitrakoot, nearby are Viradh-kund and Sharbhanga ashrama visited by them [Ref: holydham.com].
From Rishi Sharabhanga's ashrama, travelling a long way in the Dandaka forest crossing many rivers they reach Rishi Suteekshna's ashrama. Then, they pass many mountain peaks, forests, streams and rivers and live 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].
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 in Parnasala.
But, there is also 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 [Ref: ramyatra.com; Tripadvisor.in].
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.
[Source: 'Essence of the Fifth Veda' by Gaurang Damani pages 9-12].