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.
I formulated a little problem. Care to solve it?
You are given the following information:
Your task is to hide a coin in your house (or any familiar finite environment).
After you've hidden the coin your memory will be erased and restored to a state just before you receiving this information.
Then you will be told about the task (i.e that you have hidden a coin), and asked to try to find the coin.
If you find it you'll lose, but you will be convinced that if you find it you win.
So now you're faced with finding an optimal strategy to minimize the probability of finding the coin within a finite time-frame.
Bear in mind that any chain of reasoning leading up to a decision of location can be generated by you while trying to find the coin.
You might come to the conclusion that there cant exist an optimal strategy other than randomizing. But if you randomize, then you have the risk of placing the coin at a location where it can be easily found, like on a table or on the floor. You could eliminate those risky locations by excluding them as alternatives in your randomization process, but that would mean including a chain of reasoning!