Delhi

City · 501 BCE · in South Asia

Capital of Mamluk Dynasty (1210–1290), Khalji Dynasty (1294–1320), Tughlaq Dynasty (1326–1413), and 4 more.

Bordeaux (501 BCE): Capital of Duchy of Gascony (768–1065).
Khiva (502 BCE): Capital of Khanate of Khiva (1512–1919).
Nanjing (495 BCE): Capital of Eastern Wu (229–265), Southern Tang (960–976), Ming Dynasty (1375–1644), and 2 more.
Pasargadae (c. 550–330 BCE): Capital of Achaemenid Empire (550 BCE–330 BCE).
Ecbatana (c. 550 BCE – c. 1800 CE): Capital of Achaemenid Empire (550 BCE–330 BCE).
Seuthopolis (c. 450–338 BCE): Capital of Odrysian Kingdom (450 BCE–338 BCE).
Ujjain (c. 600 BCE – c. 405 CE): Capital of Janapada of Avanti (600 BCE–405 BCE), Western Satraps (43–405).
Mathura (c. 600 BCE): Capital of Janapada of Surasena (600 BCE–405 BCE).
Milan (600 BCE): Capital of Duchy of Milan (1402–1539), Ambrosian Republic (1450–1450), Cisalpine Republic (1797–1799).
Varanasi (c. 600 BCE): Capital of Janapada of Kasi (600 BCE–451 BCE).

Around the same time and place

Gautama Buddha (c. 563 BCE – 483 BCE): Founder of Buddhism, born at Lumbini in present-day Nepal. His traditional dates are c. 563–483 BCE; many scholars place his death around 400 BCE.
The Buddha’s enlightenment (c. 528 BCE): According to tradition, Siddhartha Gautama attained enlightenment under the Bodhi tree at Bodh Gaya, the founding moment of Buddhism.
Mahavira (c. 599 BCE – 527 BCE): The 24th Tirthankara of Jainism, who systematised Jain teaching in the Ganges plain. Traditional dates are 599–527 BCE; some scholars place him a century later.
Vedic period (c. 1,500–500 BCE): Period in northern Indian history when the Vedas were composed, marked by Indo-Aryan settlement of the Punjab and Ganges plain and the development of early Hindu ritual.
Mahajanapadas (c. 600–345 BCE): Sixteen great kingdoms and republics of northern India in the 6th century BCE, among which Magadha eventually became dominant.
Ramayana (c. 500 BCE): Sanskrit epic attributed to Valmiki, telling the story of Rama of Ayodhya; its composition is usually placed between the 5th century BCE and the early centuries CE.
Pataliputra (c. 490 BCE): City on the Ganges founded as a fort by Magadha around 490 BCE; it became the capital of the Maurya and Gupta empires and is modern Patna.
Vaishali (c. 600–481 BCE): Capital of Janapada of Vajji (600 BCE–481 BCE).