This one is easy, as long as I look outside the US..Here are some old buildings from India, Italy and Turkey.Amber Fort, Jaipur, India (built in 1592)
The Colosseum, Rome, Italy (built in AD 80)
The Sultanahmet Mosque, Istanbul, Turkey (built in 1609)
Hawa Mahal, Jaipur, India, built in 1799