I always wondered why the US didn't nuke Japanese military bases instead of major cities. Would have made the same impression on the Japanese government with far fewer civilian casualties.
The primary target for Fat Man was Kokura; Nagasaki was an alternate. As for its military importance, to quote Wikipedia:
"The city of Nagasaki had been one of the largest seaports in southern Japan, and was of great wartime importance because of its wide-ranging industrial activity, including the production of ordnance, ships, military equipment, and other war materials. The four largest companies in the city were Mitsubishi Shipyards, Electrical Shipyards, Arms Plant, and Steel and Arms Works, which employed about 90% of the city's labor force, and accounted for 90% of the city's industry."
"The city of Nagasaki had been one of the largest seaports in southern Japan, and was of great wartime importance because of its wide-ranging industrial activity, including the production of ordnance, ships, military equipment, and other war materials. The four largest companies in the city were Mitsubishi Shipyards, Electrical Shipyards, Arms Plant, and Steel and Arms Works, which employed about 90% of the city's labor force, and accounted for 90% of the city's industry."