Since artillery units require one level of Men (= population) in addition to resources, it makes the most sense to build them in cities with higher levels of Men -- in the case of the CSA, that's Richmond or Memphis. Memphis strikes me as too risky, because even though well fortified it might be taken more easily than Richmond. And Richmond already has a Manufacturing Center, so building another there would speed up the time of production even more. Unfortunately, I cannot build any new buildings in Richmond until I've first build a Plantation or Mansion. So, I instead settle on Norfolk, which has just 3 Men and therefore cannot produce more than three artillery units per year (i.e., not until the April population refreshment restores it to its maximum level). Of course, artillery is expensive enough that I'd be unlikely to build more than three units there anyway, and I do have other cities in which I can build them.
There is a plus to putting the new building in Norfolk: there are three foundries there, and each foundry gives a new artillery unit +.2 quality, so the artillery brigades I produce in Norfolk will be of a high quality than those built elsewhere.
(I should note that manufacturing centers also speed up the process of producing new infantry brigades, but I don't really care about that -- those take only four turns to produce, which isn't bad. I'd much rather use the scarce Men resources for artillery. But still, if ever one is in a pinch, it might be very useful to have a seasoned infantry brigade appear after three turns instead of four. I just don't plan on being in such a pinch...)