the Pantheon in Rome has been in continuous use as a church or temple since it was built in about 126 CE.
The Maison Carre is older, having been built circa 16 BC. It's the best really complete temple from the classical world that still exists, and it was turned into a Church, too. It still functions as a museum.
Theatre_of_Marcellus, Julius Caesar started building it; it was first used for performances in 17BC, finished 12BC, used variously as a theatre, then fortress, then residences.
Ye Olde Fighting Cocks is a public house in St Albans, Hertfordshire, which is one of several that lay claim to being the oldest in England, 800 years. It currently holds the official Guinness Book of Records title, but Ye Olde Man & Scythe in Bolton, Greater Manchester has claimed it is older by some 234 years.
Qufu Confucius Temple (Kong Miao). The Temple started as three houses in the year of 478 BC, the second year after the death of Confucius, in continuous use, today it's a museum of culture.
A few years back, Dutch architects Merkx + Girod converted a Dominican church into one of the coolest bookstores ever, the Boekhandel Selexyz Dominicanen in Maastricht was built in 1294.
Temple of the Flourishing Law) is a Buddhist temple in Ikaruga, Nara Prefecture, Japan. Its full name is Hōryū Gakumonji, or Learning Temple of the Flourishing Law, the complex serving as seminary and monastery both. It was built in 607 burned then rebuilt in 711.
The Pickman house in Salem MA. was built in 1664, it serves as the nations oldest continuously operated museum today.
Gonzalez-Alvarez House in St. Augustine, built in 1723, adaptive reuse as a museum.
Bottom line, with every brick that comes down/came down in Jacksonville, we lose irretrievable history. There is just no reason for our city to continue this destructive course.