What should I do if I don't know where the laundromat is to which the deceased owes money, and I don't know his friends who might know its location, and must I continue searching until I find someone to pay off his debt to?

The debt of the deceased must be paid from his estate, and the debt delivered to its owner. If you are unable to reach the owner of the debt, then charity should be given on his behalf equal to the debt. As long as you are an agent for the deceased's father in delivering the money to the debt's owner, you must search for him by all possible means. If you do not find him, then inform the deceased's father so that he may act.