Born on US Naval Base in Philippines: Father American, Mother Filipino-citizen or no?

My best guess is that you are, indeed, a U.S. Citizen.

Look at USCIS - Citizenship Through Parents

Citizenship Through Parents

Whether someone born outside the United States to a U.S. Citizen parent or parents is a U.S. Citizen depends on the law in effect when the person was born.

These laws have changed over the years, but usually require a combination of at least one parent being a U.S. Citizen when the child was born and having lived in the U.S. Or its possessions for a period of time. Additionally, children born outside the United States may become citizens after birth based on their parent’s citizenship or naturalization. For further information on this topic, please see the links to the left under citizenship through parents.

If you still need assistance after having viewed these pages, please contact us at our National Customer Service Center. See the “Contact Us” link to the right.
*****************
I'll alert several people on this site to give you more information as to how to obtain your birth records. Your Navy father is the key.