Kīkaṭapura was the city that Bhagavān Kalki marched against in his first great campaign. He went there to gain wealth for the Aśvamedha-yajña (horse sacrifice) of Vishṇuyaśas. The Kalki Purāṇa describes it as a stronghold of Buddhist adharma (wrong living) in the Kali Yuga.

Its king was Jina. He fought Bhagavān Kalki with two akshauhiṇī armies (an akshauhiṇī is a very large army) before he was slain.

How the city lived

The Kalki Purāṇa, Dvitīyāṃśa, Chapter 6, describes Kīkaṭapura as a city that had turned away from Vedic dharma in every way.

Vast Buddhist temples (bauddha-devālayāni) covered the city.
No pitṛtarpaṇa (water offering to the ancestors) was made. The ancestral rites were wholly absent.
No devapūjā was done. The devas received no worship.
The people argued that paraloka (the world after death) does not exist.
They held that the deha (body) itself is the ātmā.
All of them reasoned by tarka (logic and argument) and not by śruti (the revealed Veda).
There were no jāti or kula niyamas. No varṇa-dharma distinctions were kept.
All were rich. All were devoted to women, food and drink. All were nāstikas (those who reject the Veda).

Kalki’s campaign

Bhagavān Kalki marched to Kīkaṭapura to obtain wealth for the Aśvamedha of Vishṇuyaśas and to set dharma in its place again. He entered the city with his army.

The battle with King Jina was the central event of this campaign. After it came the battle with Śuddhodana, who brought Māyādevī. Jina was killed, and Māyādevī merged into Bhagavān Kalki. The Buddhist forces were then destroyed. Bhagavān Kalki took the jewels and wealth of the defeated city and returned to Śambhala. (Kalki Purāṇa, Dvitīyāṃśa, Chapters 6–7)

The name

The name Kīkaṭapura recalls the Kīkaṭa country, which the Ṛgveda mentions as a region of non-Ārya practice.

Sources

Kalki Purāṇa, Dvitīyāṃśa, Chapters 6–7
Ṛgveda (the mention of the Kīkaṭa country)