To those from the Western hemisphere, it’s always fascinating to hear that some homes and businesses from the times of the Greek philosophers still have inhabitants, and then you remember that the Western hemisphere is itself not without its own examples, for example some Mexican villages still have temples from the times of the Mayans.
There are archaeological finds of buildings from more than 9000 years ago (oldest in the region).
There’s a church that was finished sometime during the 1200s and is preserved in its original form in the municipality, but technically it’s not within town limits.
The main church was also initially built around that time but was rebuilt in the late 1700s - nothing of the original remains.
The cellar of a royal farm still remains, which was built in 1552, though it’s more a ruin than a building.
A castle/royal manor was built in 1652, and although it has been renovated and expanded in the early 1700s, parts of the structure are still from the original.
So, I suppose it depends on what you’re looking for.