I have read that Ramakrishna Paramahamsa would often teach devotion to less advanced disciples but would only teach Advaita to Vivekananda. Did Vivekananda worship any personal deity?
Yes, He did. He worshipped Maa Kali. But He never taught Kali worship to anyone. He considered being His personal affair. He mentioned: "The secret of my Kali-worship will die with me".
He wrote a beautiful poem: Kali the Mother:
The stars are blotted out,
The clouds are covering clouds,
It is darkness vibrant, sonant.
In the roaring, whirling wind
Are the souls of a million lunatics
Just loose from the prison-house,
Wrenching trees by the roots,
Sweeping all from the path.
The sea has joined the fray,
And swirls up mountain-waves,
To reach the pitchy sky.
The flash of lurid light
Reveals on every side
A thousand, thousand shades
Of Death begrimed and black —
Scattering plagues and sorrows,
Dancing mad with joy,
Come, Mother, come!
For Terror is Thy name,
Death is in Thy breath,
And every shaking step
Destroys a world forever.
Thou "Time", the All-Destroyer!
Come, O Mother, come!
Who dares misery love,
And hug the form of Death,
Dance in Destruction's dance,
To him the Mother comes.
He also wrote one beautiful hymn: Amba-Stotra in Sanskrit.
Ref:1. Nivedita Lokamata,Sankari prasad Basu, Vol 1.page 298-300 2.CW of Swami Vivekananda
Swami Vivekananda's devotion towards Goddess Kali is mentioned in his short biography too.
Here is the PDF (A short biography of Swami Vivekananda by Swami Tejasananda).
Following the pilgrimage to Amarnath the Swami’s devotion concentrated itself on the Mother, and he was soon blessed with a wonderful vision of Kali the Divine Mother. While his vision was most intense he wrote ‘Kali the Mother’—a poem, where he is seen at his best. After this experience he retired alone abruptly on September 30 to the Coloured Springs of Kshir Bhavani where he practised severe austerities. He was found completely transfigured when he returned to his disciples after a few days.