Actually the test was closer Socorro and the small town of San Antonio, NM (birthplace of the Hilton dynasty.) It was on what is now White Sands Missile Range which is very close to Alamogordo, but there is a mountain range between the test site and Alamogordo. The blast was visible from San Antonio though.

I would add that Alamogordo was the fictitious location of the giant ants in the film "Them!"

They open it once a year but you can see the site as you drive by. Very close to the outskirts Socorro, although WSMR is so large it covers both sides of the range if I'm not mistaken.