Vibhishana requested Rama to stay for some time so that he can honour Rama properly. Rama insisted that he must return since Bharata will not wait even day longer once 14 years are completed. Vibhishana offered a Pushpaka Vimana so that Rama and Sita can return quickly. Rama was pointing out the various places that he and Lakshmana had travelled.

Sita requested Rama to stop in Kishkinda so that she can meet Tara and other vanara ladies. Like Sita, they too had been away from their men for a long time. Sita said who can understand their anguish better than me and that she would like to take them along to Ayodhya for the return ceremony. They stopped at Kishkinda and then also at Bharadwaj Rishi’s ashram.

Picture Credit: J Martin and Manoj Publications

Rama wanted to know if Bharata was really willing to relinquish the kingdom. He wanted to be sure that Bharata wanted Rama to return. So Rama asked Hanuman to go to Ayodhya and inform Bharatha that he is on his way. Hanuman, in the guise of a Brahmana, went to see Bharatha. Bharatha was living the life of a monk, although he was the ruler of a large kingdom. He was staying in a small hut, always chanting Rama's name, along with Shatrughna and the ministers. Hanumanji informed him of Rama’s impending return.

Hearing this, Bharatha fainted for a moment and was then exhilarated. He wept the tears of joy. Bharatha told Shatrughna to decorate the city commemorating Rama's return. He wanted the citizens to show up with their families and look at their real king.

Picture Credit: J Martin and Manoj Publications

The coronation of Rama was carried out spectacularly. Rama gave precious gifts to everyone. To Sita, he gave a special necklace with gems so precious that its value cannot be assessed. She put it on her neck first and smiled at Rama. Then she took it out with both her hands, looking at Rama, and then looked at Maruti and the necklace. Rama knew what she wanted to do and told her: "O Beautiful One! Look around and you may gift it to anyone you like." Sita smiled and gifted it to Hanuman. Hanuman wore it with pride and stood with folded hands, and his face glittered along with the stones in the necklace.

Picture Credit: Prasad and Guruvayoor Devaswom

Rama called Hanuman aside and asked him what book he would want. Maruti replied with a devotion-filled voice: "Lord, please let me live till the day your name and fame are sung by the people all over the world. My thirst in hearing your name and glories has not been satiated yet and I do not want any other boon. May my mind be always devoted to you!"

Rama blessed him and said "May you live long as desired, liberated, listening to my stories. My friend, devotion is the only path to realization! Liberated, you will remain in this world till the end of the Kalpa. At the time of the dissolution of the world, you will attain to oneness with me.” Sita also blessed him that all enjoyable things of life will follow Hanumanji wherever he was. Hanumanji prostrated before them again and again before leaving for the Himalayas for penance.

Picture Credit: Swami Raghaveshananda and RK Mutt

In Valmiki Ramayana, Hanumanji does not go to the Himalayas to do penance, like it is narrated in Adhyatma Ramayana. He also does not seek to live as long as the story of Rama is told. He returns to Kishkinda with Sugriva.

Additional Source: Adhyatma Ramayana by Lala Baij Nath

Picture Credit: J Martin and Manoj Publications

Adhyatma Ramayana was given by Shiva to Parvati. It has all the profound truths about Rama. Shiva had repeatedly churned the whole of Vedas. He realized that the supreme Brahman is Rama or Vishnu whose form cannot be known. Shiva, after realizing this, has extracted the essence and put it in Adhyatma Ramayana clearly in a brief form and communicated it to Parvati.

Additional Source: Adhyatma Ramayana by Lala Baij Nath

Picture Credit: Swami Raghaveshananda and RK Mutt

By the time Ravana was killed, Lanka had been devastated. Vibhishana sought a blessing from Rama to build a new capital on the western coast and chose Kelaniya, near Colombo. A Buddhist temple is at the site of Vibhishana's palace and houses the only temple to Vibhishana in the world. There are deities of Vibhishana in temples near Rameswaram but those are not solely dedicated to him. The coronation of Vibishnana by Lakshmana is also represented in a sculpture in Kelaniya.

Source
Footsteps of Rama, Vikrant Pande and Neelesh Kulkarni.
Ramayana in Lanka

Picture Credit
https //kelaniyatemple.lk/

Bharat ruled from Nandigram during Rama's exile. When Rama was returning to Ayodhya, he did not want to claim the kingdom against Bharat's wish. Therefore he sent Hanuman to assess the intent of Bharat. Hanuman came in disguise as a Brahmin and tested Bharat's will to welcome Rama.

The temple here shows Bharat and Hanuman in embrace after Hanuman revealed to Bharat his true form. The Jata Kund here is believed to be the place where Lord Rama and Lakshman cut their matted hair at the end of their exile.

Source
Footsteps of Rama, Vikrant Pande and Neelesh Kulkarni.
Uttar Pradesh A to Z, UP Tourism