Kokura was the site of a major arsenal. It actually shows up in their second target meeting discussion:

(4) Kokura Arsenal - This is one of the largest arsenals in Japan and is surrounded by urban industrial structures. The arsenal is important for light ordnance, anti-aircraft and beach head defense materials. The dimensions of the arsenal are 4100' x 2000'. The dimensions are such that if the bomb were properly placed full advantage could be taken of the higher pressures immediately underneath the bomb for destroying the more solid structures and at the same time considerable blast damage could be done to more feeble structures further away. (Classified as an A Target)

So you have to see this as having two benefits: one is that it a good strategic target because it is a military arsenal surrounded by an urban area. That means it satisfies their "bomb a military target but also do a lot of collateral damage" requirement, so that the power of the bomb is showcased. And it also was relatively flat, so the damage would go a far distance.

Nagasaki wasn't discussed in any of the target meetings; it was lower on the list than any they got to. In fact, it was so low on their agenda that it wasn't even put on a "reserved list" for protection against firebombing in late June 1945, when Kokura was (the list had previously included Hiroshima, Kyoto, and Niigata). After the bombing, the supposed importance of Nagasaki as a military target was talked about at length to justify the bombing, but the actions at the time suggest that nobody really thought it was that important a target.

In fact, it's not even totally clear when it ended up on the target list. The original list was Kyoto, Hiroshima, Yokohama, Kokura, and Niigata. Kyoto got removed at personal intervention of Secretary of War Stimson. Yokohama got firebombed shortly after the list was compiled. So that left Hiroshima, Kokura, and Niigata. Nagasaki shows up on a July 24 target list that is what gets approved by Truman et al., but not before that. That list simply says that Nagasaki is "a major shipping and industrial center of Kyushu," whereas it claims Kokura was "one of the largest army arsenals and ordnance works; has the largest railroad shops on Kyushu; and has large munitions storage to the south."

I haven't found documents referencing it, but the fact that Nagasaki was hilly may have played a role in its being a secondary target as well — hills can amplify the effects of the bomb within them, but limit its ultimate reach. They were interested in destroying as much area as possible, not just destroying the destroyed area more intensely. The effect of hills was anticipated (and you can see it in the early discussions of the advantages of Kokura), and did indeed limit the scope of Nagasaki's destruction (also contributed to by the fact that the bomb was off-target significantly).

As an aside, the source of the cloud/smoke/haze at Kokura has not been conclusively determined.

Of interest might be this recent story, about how a group of steel workers actually created those clouds by burning coal tar to create a smoke screen, saving their city Kokura at the expense of Nagasaki.

Why not drop the bomb right on top of the emperor, wherever he resided?

Can I ask a question off this question. Are their any good reads on the aftermath of Nagasaki ? I see so much about Hiroshima . I'm looking for the aftermath and rebuilding process.