is there any way to find a paternal father if name and where abouts is unknown..known facts of mothers possible city residence

i have a 2 1/2 year old daughter ehos paternal father was one night thing..i never got his phone number.and due to being horrible with names dont have that either. i know the city his mother sister and step father live in his description but thats about it. i have worked with childsupport to locate him but havehad no sucses..i am open to anythiong to locate him no matter the embarassment.i fear if my child would ever need medically anything im not able to provide someday like bonemarrow say i also truley believe if he would want to know as it was my descion not to persue anything more than that one night and wake up everyday feeling like a faulire im at a lose what to do i dont want my daughter to pay for my poor judgement - Is this your question? Add additional information