The St. Louis Country Library does not have fax machines for public use at this time.
There may be a number of places where you can use the fax facility by paying nominal charges. A lot of general stores and drug stores sometimes buy a fax machine and make it open to public use at a price per fax that you send. So, the best way could be to ask around when you visit a store or a shopping centre. If you are a member of the St. Louis Public Library, you could use the fax machines there. You have still got to pay a nominal charge for each fax that you send though. A lot of internet cafes have fax machines too.