Ursuline Academy is the first and oldest school for girls in the United States.
It was founded in 1727 in New Orleans, Louisiana, by Ursuline nuns. The original building for the school, now known as the Old Ursuline Convent, still stands on Chartres Street in the French Quarter and is the oldest building in the Mississippi Valley.
From 1912 until the time of this writing, Ursuline Academy has been located in Uptown New Orleans on State Street. Ursuline nuns still live there, so I guess that makes it a convent too.
Note there's another Ursuline Academy in Wilmington, Delaware, another in Cincinnati, Ohio, another in Dallas, Texas... The Roman Catholic Order of St. Ursula has certainly been busy.