I know the compliance officer needs to be able to report to the board of directors, but who should be over the compliance officer for day to day operations?

Depends on your bank size and structure. At my old bank, I was the CO but also VP and sat on the board, so it was just the board over me in that function. Technically the President was over me as well, but not in my compliance role (though effectively he was, it just wasn't spelled out that way).

Depends on the size and risk of your Bank. I've seen CO's report to CCO's and CRO's either of which is appropriate.

Same. It depends on size. I have been at bank's where the CO's report to the CCO and where they report to the CRO.

As others - depends on the size and complexity of the bank.
Generally someone high enough in the structure so compliance is taken seriously. Not heads of operations or loans - possible conflict of interest