Pretty sure "The Girl From NYC" was recorded entirely at Western, vocals and all.
Based on the evidence on UM 9, I think you're right. But that's not what AGD says on Bellagio 10452:
May 24 - Summer Days... session: You're So Good To Me/The Girl From New York City/
I'm Bugged At My Ol' Man /And Your Dream Comes True vocals [Columbia]

The May 24 date was provided for all of these titles in the liner notes of the Capitol twofer reissue. I've often wondered about the accuracy of that date, but it's not out-of-the-question that there were two sessions that day: "The Girl From NYC" basic track was cut an 8:30pm-11:30pm session at Western, but the vocals weren't neccessarily done that day. And vocals for the other songs mentioned above could easily have been recorded earlier in the day at a single Columbia Studios session.