Q. Where can I find some primary sources about Ponce de Leon's search for the Fountain of Youth?

None of de Leon's logs from his exploration of Florida have survived to the present day.  The most primary source relating to this voyage is Historia general de los hechos de los Castellanos by Antonio de Herrera, a 16th century Spanish historian who used the ship's original logs to write an account of the voyage. 

Historia was written in Spanish, and its text can be found through Google Books. 

An English translation of the section of Historia that relates to de Leon's Florida expedition, along with translations of other early writings related to the journey, is available at American Journeys.