I think I would write down a list of places where, if I had hidden it there, they would be hard to find even if I knew where to start looking, (my house has a fair number of these,) assign numbers to each, and then roll a die and hide it in the one with the corresponding number.

I'd probably assign individual numbers to options like "hidden amongst the belongings in any drawer in the house which I do not use regularly," and determine which one to use by number assignment and random number generator if I rolled that option.