According to a hadith cited by Wikipedia, Eid al-Fitr and Eid al-Adha were initiated in Medina.
The tradition concerns Muhammad’s arrival in Medina after the Hijra, his migration from Mecca. A report attributed to Anas ibn Malik says that Muhammad found the people of Medina observing two days associated with recreation. Muhammad then taught that God had replaced them with two prescribed festivals: Eid al-Fitr and Eid al-Adha.
Medina therefore supplies the canonical answer in this question’s wording. Mecca is a major Islamic holy city and the destination of the Hajj, while Jerusalem and Damascus are also important cities in Islamic history, but this particular hadith narrative identifies Medina as the setting where the two festivals were established for the Muslim community.
Eid al-Fitr is celebrated on 1 Shawwal after Ramadan. Eid al-Adha begins on 10 Dhu al-Hijjah during the Hajj season. The two festivals are distinct in timing and emphasis, but both include congregational prayer, communal celebration and charitable concern.