Where and when?

Kumbha Mela is a mammoth fair where saints and devotees gather. Kumbha Mela is celebrated at the aforesaid four places depending on the positions of planets and stars.
When Jupiter (Guru) and Sun are in zodiac signLeo(Simha Rashi) it is celebrated in Trimbakeshwar, Nashik. 
When Sun is in zodiac sign Aries (Mesha Rashi) it is celebrated at Haradwar 
When Jupiter is in zodiac sign Taurus (Vrishabha Rashi ) and Sun is in zodiac sign Capricorn (Makar Rashi) Kumbha Mela is celebrated at Prayag 
When Guru and Sun are in zodiac sign scorpio (Vrishchik Rashi) the Mela is celebrated at Ujjain. 
Recognizing the importance of the Sinhastha Kumbha Mela Shri Shankaracharya appealed the disciples of his Vaidik Dharma to assemble at the time of Sinhastha Kumbha Mela. Following his appeal, till now devotees, pilgrims, and people of various sects and religions gather together for Kumbha Mela.
In Kruta Yuga, Durwas Rishi saw Indra - the King of Gods - sitting on elephant Airawat. Durwas was pleased to see Indra and presented him a chain. However Indra did not accept the present . It fell down and was trodden by elephant Airawat. Durwas Rishi got upset due to this and cursed Indra. As an effect of the curse, all Gods lost their powers and had to often lose a battle against Danavas (Demons). So all Gods including Brahmadeva surrendered themselves to God Vishnu to get back their power. Vishnu suggested them to approach Danavas and persuade them to perform Samudra Manthana (churning of the sea). He said Samudra Manthana will bring out Amruta , which will bring back your power and you will not be efeated by Danavas. So Samudra Manthana was carried out.

One of the many precious things that arose from the depths of the troubled waters was a pot of nectar (Amrit Kumbh). Lord Vishnu, disguising himself as an enchantress ( Mohini), seized the nectar from the demons. While fleeing from the evil ones, Lord Vishnu passed the nectar on to his winged mount, Garuda. The demons finally caught up with Garuda and in the ensuing struggle, a few drops of the precious nectar fell on Allahabad, Nashik, Hardwar and Ujjain. Since then, the Kumbh Mela has been held in all these places, every 12 years.
Another story is that once all the Teerthas went to Adinath Bhagwan Shankara . Following Bhagwan Shankara’s order they had been to Mrutyuloka (earth) to save sinners on earth. Teerthas absolved the sinners on the earth, but were themselves saturated with others’ sins . They requested Bhagwan Shankara to free themselves from sins. Shankara asked them to go and live in solitude for one year at the bank of river Godavari. Shankara promised the Teerthas that he himself, with all other Gods will also stay with them . After taking bath in the sacred water of Godavari, they will be free from the sins.
Hence during the Kumbha Mela a dip in Godavari river has attained a great importance.
In Shiva Purana there is a story explaining the importance of Sinhastha Kumbha Mela. Gautama Rishi got salvation of his cow-killing sin from Lord Shankara after a long penance. Then the river Ganges descended down on the earth. After some time she wanted to go back to her home place. However the Rishis and Gods gathered there and requested her to stay back on the earth for the prosperity of the earth. She agreed to stay back only after taking a promise from Lord Shankara that all the Rishis present there and all Gods will stay with her. Then only she will stay back. Gods and Rishis promised her that during the period, when Jupiter and Sun will be in the zodiac sign Leo (Simha Rashi), they will all stay on the earth.
In later years , it is said , acknowledging importance of Kumbha Mela Lord Rama with his Guru Kashyap stayed and lived for one year in Trimbakeshwar. During this period he performed all the religious rites like yatra, shraddha etc near Kushavarta .