In context, the poetic parallelism indicates 'daughter of Zion' is intended to be read synonymously with 'Jerusalem'. Here is Isaiah 52.1-2 from the ESV, with the chiastic parallelism marked:
- A - Awake, awake, put on your strength, O Zion;
- B - put on your beautiful garments, O Jerusalem, the holy city;
- C - for there shall no more come into you the uncircumcised and the unclean.
- B - Shake yourself from the dust and arise; be seated, O Jerusalem;
- A - loose the bonds from your neck, O captive daughter of Zion.
Here is another example from Isaiah 10.32:
- A - This very day he will halt at Nob;
- A - he will shake his fist
- B - at the mount of the daughter of Zion,
- B - the hill of Jerusalem.
In this case, 'the mount of the daughter of Zion' is synonymous with 'the hill of Jerusalem'. The idiom 'daughter of (location)' is used for cities other than Jerusalem, too. Isaiah 47.1 uses the expression for the city Babylon:
- A - Come down and sit in the dust, O virgin daughter of Babylon;
- A - sit on the ground without a throne, O daughter of the Chaldeans!
- B - For you shall no more be called tender and delicate.