Jim,
Are you asking which of the two, St. A or BV, you would play, or are you open to other suggestions?
Glen Echo is an enjoyable course with the significance of having held the last Olympic golf competition in 1904. It's still pretty much as it was back then.
Of the two courses you mentioned, I much prefer BV over St. A.
Additionally, Meadowbrook, Algonquin and Norwood Hills are good courses that may allow unaccompanied play.
David