In E. coli, during lactose metabolism repressor binds to : -

In the lac operon, the regulator (i) gene produces a repressor protein.
In the absence of lactose, the repressor binds to the operator gene, which lies between the promoter and the structural genes. This blocks RNA polymerase and switches off transcription of the structural genes (z, y, a).
When lactose (allolactose, the inducer) is present, it binds to the repressor and makes it inactive, so it can no longer bind the operator, and the genes are transcribed.
So the repressor binds to the operator gene.