What is the oldest U.S. city that is also a capital?
That distinction would have to go to Santa Fe, New Mexico.
Santa Fe, which means "holy faith" in Spanish, was once a collection of Pueblo Indian villages from around 1050 to 1150. It was first inhabited by Spanish settlers on a very small scale in 1607, then truly settled by the conquistador Don Pedro de Peralta in 1609-1610. The Pilgrims wouldn't land in Plymouth, Mass. for another 10 years.
Located in the foothills of the Sangre de Cristo Mountains, 7,000 feet above sea level, Santa Fe is also the highest U.S. state capital.
You can find more information at the official site of Santa Fe.