The place was the Society for the Advancement of Judaism (http://www.thesaj.org), located at 15 West 86th Street. The synagogue was run by Dr. Mordecai M. Kaplan, and the first person to have a Bat Mitzvah was his daughter, Judith Kaplan.
I asked the Reconstructionist College about the first "Bat Mitzvah" event and received this excellent response:
I am currently writing a graduate seminar paper on the bat mitzvah ceremony at the Society for the Advancement of Judaism (SAJ), the synagogue founded by Dr. Mordecai M. Kaplan, Judith Kaplan's father. There was no secular press coverage of her bat mitzvah, which occurred on May 5, 1922, though I have not determined if it received coverage in the Jewish press (Anglo or Yiddish).
The first reference to the "bas mitzvah" ceremony I have thus far encountered is in minutes of the SAJ Board of Trustees from early February 1922, shortly after the congregation was organized. Dr. Kaplan informed the Board of his intention to introduce such a ceremony and let them know that he intended that his eldest daughter to be the first, and the Board assented with great enthusiasm. I have not yet had an opportunity to review Kaplan's diary to determine if he wrote about the ceremony using this terminology earlier than that date, though if you check in with me again in a few weeks I hope to have made some headway on the diary. I can also email you the precise date and language from the minute books if this is helpful.
The synagogue standardized the usage to the Sephardic pronuciation "bat" mitzvah some time in the 30s.
Rabbi Deborah Waxman
Assistant to the President and Director of Special Projects
Reconstructionist Rabbinical College
1299 Church Road
Wyncote, PA 19095