Which city was the capital of the Achaemenid Persian Empire's ceremonies?

Persepolis, which was ceremonial rather than administrative - the empire was run from Susa, Babylon and Ecbatana, and Persepolis existed for ritual, particularly the new year festival at which subject peoples brought tribute.

The staircase reliefs show that procession, and they are unusual in what they do not do. Delegations from twenty-three nations bring gifts in their own dress, guided by Persian ushers who hold their hands - and nobody is depicted kneeling, bound or trampled, which is the standard iconography of every other ancient empire. The Achaemenids advertised their empire as a partnership, which is propaganda, and it is a strikingly different piece of propaganda from Assyria's flayed prisoners.

Alexander burned it in 330 BC. Whether it was a drunken accident at a party, as several sources have it, or a calculated act of revenge for the Persian burning of Athens, is unresolved and was argued about in antiquity. The fire baked and preserved thousands of clay administrative tablets, which is how we know the empire paid its workers - including women, at rates varying by skill, with extra rations for new mothers.