I would hide it in a place that is not too hard to find but really hard to reach so that my future self will stop and think about why I put it there. I (in the future) will then hopefully realize that if the task really was as told then I would have "hidden" the coin at the easiest possible place. Therefore, something about the task is wrong. As the coin is hard to reach, my past self probably doesn't want me to find it. This doesn't make sense unless one of us (past or future self) has been lied to. Having the same mental faculties as I have now, I trust that my future self will make the right decision, which may depend on the specific circumstances.
This approach is quite risky as it assumes that my future self will in fact follow the same line of reasoning I just did, but then again that is kind of the point of this task.
If it's allowed I could of course also just leave a note explicitly saying the above.
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!