I'm no expert on that particular part of Japan, but let me share my 2 cents. For brand new, look for the local Yodobashi Camera or Bic Camera if any. If you're looking for Master Shop Grand Seiko models, you'll be forced to visit a Department Store. Second hand I'm afraid I cannot help you, but I'd be surprised there's much to be found in Fukuoka...
A lot (and I mean a lot, outside of Tokyo in particular) of the second hand trade in Japan goes on online (Jackroad and Yahoo Auctions are your best bet). I'd be surprised there's a lot of second hand business in Fukuoka.
Please do share with us about your findings when you're back! We also went to learn and that part of Japan is virgin territory for me at least.
If you share with us what takes your fancy in terms of models or price ranges, others might be able to help you more specifically.
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