Posted in 1960s, Bank, Extant, TX - Galveston Moody National Bank – Galveston 2302 Post Office St. – Galveston TX (built 1962) Galveston’s Moody National Bank, founded by W.L. Moody, Jr. in 1907 as City National Bank, changed to its current name in 1953 and moved into its current home in 1962.