Which structure, built in 1800, is the oldest of the buildings where banks have been located?

The oldest structure among the options provided, built in 1800, is 343 Royal Street. This building holds historical significance as it is one of the earliest examples of a building specifically constructed to house banking operations in New Orleans. The architecture and design reflect the era's stylistic choices and contribute to the overall historical narrative of New Orleans as a financial hub in the early 19th century.

The importance of this site extends beyond its age; it embodies the evolution of banking in the region during a pivotal time in American history. This building has witnessed significant changes in the city's economy and serves as a tangible link to the past, showcasing the architectural styles typical of that period.

The other buildings listed do not have the same historical prominence or date of establishment, and they may not have connections to banking operations that date back to 1800. Understanding the historical context and architectural significance of 343 Royal Street is vital for a comprehensive appreciation of New Orleans' rich heritage.