The three cities are

Anav Mal (egoism) - Destroy the first city Anav Mala through self-surrender to Lord Shiv and consequent descent of His grace (Anugraha).

Karm (bondage of Karm) - Annihilate the second impurity, viz Karm, through consecrating the fruits of your actions to the Lord and destroying the idea "I am the doer", by developing the Nimitta Bhaav, the Bhaav that Lord Shiv is working through your various organs and that you are a mere instrument in His hands. Doing Karm with this feeling, you will not be bound by actions. You will attain purity of heart and through purity of heart, realization of Shiv Aanand or eternal bliss of Shiv.

Maayaa (the illusory power of Lord Shiv which veils the individual souls) - Annihilate the third impurity, viz Maayaa, through the recitation of Panchaakshar Mantra (Namah Shivaaya), worship of Guru, hearing and reflection of the attributes of the Lord and His various Leelaa and meditation on his form and Satchidaanand aspect.