Fathers Day - whither the apostrophe?

Despite the fact that I have no children, my Smaller Half took me down to our favourite cafe today and bought me coffee and scones.  Lovely!  It was really crowded when we got there though so I was worried we might be turned away. 

But lo and behold, knowing the staff really helps.  They directed us to our favourite table by the fire.  There was even a sign on it saying, "Reserved", so I knew that it was being saved for me.  After all, I can be outgoing when the mood strikes me, but on the whole I am more introverted than not.

Sitting sipping our coffee and nibbling on our scones made me wonder - where does the apostrophe belong in the phraselet "Father's Day"?  Is it the day of the father - Father's Day?  Or is it the day of all fathers - Fathers' Day?  I lean towards the latter even though the spirit of the day is more the former.

I hope you've all had a good Fathers' Day.  If you're lucky enough to still have a father around, make sure you tell him how important he is to you.