The closest is Ajlun Castle, 28 km south-west of the city centre; the most famous is Beaufort Castle (Lebanon) — #169 of 8,133 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 (15), Jordan (6), Palestine (3), Lebanon (3), Syria (1).