The fed's policies affect every area of the financial system. Can't put it in a bank because they'll almost certainly be above the insured amount and will have an incentive to bail out that bank if it's in trouble, another conflict of interest.
Perhaps some special account at the fed that pays a specific interest rate and is fully insured? But then why do Fed presidents get special access to such an account that normal folks don't?
I don't know that there is anywhere he could put his money and be above reproach, him putting his money in muni's seems like a good faith effort to do that though.