Tim Rice just liked "B. A." for "Buenos Aires," and he thought of "Big Apple." This was the 1970s, when "Big Apple" was being strongly revived as the nickname for New York City.
Buenos Aires does not have a prior tradition of being called the "Big Apple." Tim Rice made it up.
I did visit Buenos Aires, see a place called "the Big Apple" there (it was New York City-themed), walk back to the Washington Monument look-alike in the center of town, have someone smear junk all over my clothes, have people immediately help to clean it off, and have someone take my wallet. I lost more money in those five minutes in "B.A." than I ever made from solving "the Big Apple." (And I wasn't carrying much money on me, either.)
The lyrics for "Eva Beware of the City" are on several web sites, such as this one:
http://media52.fastclick.net/w/safepop.cgi?mid=44164&sid=964&id=102909&len=0&c=26&nfcp=1&fp=2
[Eva:]
I wanna be a part of B.A.
Buenos Aires, Big Apple
[Eva's family:]
She wants to be a part of B.A.
Buenos Aires, Big Apple

