The closest is Ajlun Castle, 28 km south-west of the city centre; the most famous is Beaufort Castle (Lebanon) (#165 of 9,035 worldwide) 91 km north. The oldest dated site in the circle is Amman Citadel, founded 1800 BC.
The 100 km circle reaches into 5 countries: Israel (14), Jordan (6), Palestine (3), Lebanon (3), Syria (1).