Where does the initiator tRNA sit on the ribosome?

I think what you meant was

"Where does the initiator trNA BIND on the ribosome?"

if so,

The initiator tRNA's function is to bring amino acids to the ribosome during translation. tRNA will bind at the A, P and E sites of ribosomes. The A site will bind to aminoacyl-tRNA which was signaled by the codon that is binding to that site. The codon will also signify the next correct amino acid that will be in the peptide chain.