There were some Rakshasas like Vibhishana who were noble. Were there any Asuras/Rakshasas who were initially evil but eventually became good i.e moved to the side of Dharma?
Brahma then addressed Vibhishana, 'O my son, I am much pleased with thee! Ask any boon thou pleasest!' Thereupon, Vibhishana replied, 'Even in great danger, may I never swerve from the path of righteousness, and though ignorant, may I, O adorable Sire, be illumined with the light of divine knowledge!' And Brahma replied, 'O scourge of thy enemies, as thy soul inclines not to unrighteousness although born in the Rakshasa race, I grant thee immortality!'
Vibhishna asked Brahma that he should always be righteous and have the light of divine knowledge. Brahma was so pleased that in addition, he even bestowed immortality upon him.
Asuras/Rakshasas/Daityas/Danavas who were initially evil but eventually became good i.e moved to the side of Dharma?
Hidimva or Hidimbi or Hidimbā
She is mentioned as the female cannibal in The Mahabharata, Book 1: Adi Parva: Hidimva-vadha Parva: Section CLIV.
But after marrying Bhima she became good. As per this wiki, currently there are a few temples dedicated to Hidimbā Devi.
Initially, Malyavan (Ravana's maternal grandfather's brother) was king of Lanka. He was not good to the deities, sages, and ascetics. When they complained about Malyavan and other Rakshas to Vishnu, Malyavan attacked on Devas with his brothers Mali and Sumali where Mali was killed by Vishnu and other two left Lanka and started living in Rasatala. Later on Kubera started living in Lanka till Ravana took it from him. -UTTARA KANDA of Valmiki Ramayana
But in Rama-Ravana war, Malyavan preaches Ravana. -Yuddha Kanda - Sarga 35 of Valmiki Ramayana
Bāṇāsura: Story is given in Śrīmad-Bhāgavatam (Bhāgavata Purāṇa) » Canto 10 .63
Asuras/Rakshasas/Daityas/Danavas who were of virtuous nature:
Shachi (queen of Indra), the daughter of Asura Pulaman (as per Mahabharata)
Bali Maharaj (as per most of the Puranas)
Prahlad (as per most of the Puranas)
Prahoti (as per Ramayana)
Vibhishana (as per Ramayana)
Vajrang, Diti's son and TARAKASUR's father (as per Shiva Purana)
Mandodari, daughter of Maya Danava (as per Ramayana)
The obvious interpretation of the Shiva Purana is Vajrāṅga is an Asura who stopped being evil on his own. However, technically the only verse he is referred to as an Asura could be interpreted as giving up his Asura form.