(1) You always hear it wrongly repeated that the first nuclear bomb was tested at Alamagordo but Alamagordo is 100 miles from the Trinity Site. San Antonio, NM was the closest settlement.
(2) Conrad Hilton, founder of the hotel chain, was born there (in his autobiography "Be My Guest" he talks about riding his horse up to Socorro, where I went to undergrad school)
(3) The Owl Bar and Cafe still serves a great green chili cheeseburger