Seeking any information on my grandmother

I recently discovered who my grandmother is from doing the ancestry.com DNA test.  My father was adopted and he never knew anything other than his birth father was in the US military and his birth mother was from England.  After communicating with a man I matched with in DNA, we realized it was his mother that gave birth to my father.  He had found a photo of a US soldier with a last name I also matched with on ancestry, along with her passport showing she had traveled to the US in July 1947, almost 9 months before my father was born in May 1948, and her final destination was Alexandria, VA where he was as born.  Unfortunately, neither side of my father’s birth parents knew anything about his existence...so I’m trying to unravel more of the story while she was here...where to search for possible documents.  Her son found something with a stamp from the National Registration Office.  And we know the address she stayed at.  Any help would be greatly appreciated