On which organ or tissue does leptin primarily act

Hypothalamus is the answer

Leptin primarily acts on the hypothalamus.

It is because its main function is to regulate energy balance by inhibiting hunger and hypothalamus is a centre for controlling appetite and food intake. Leptin receptors are located in the arcuate nucleus of the hypothalamus. Leptin is synthesized in the adipose tissue and it is opposed by the actions of the ghrelin hormone.