They say the Kindle will be sold at Joshin, Kitamura, K's Denki (all electronic retail chains), and a selection of TSUTAYA locations (a large video rental chain with its own line of ebooks).
I'm not sure that "Department Store" is an accurate translation, since I've never seen much of an electronics selection in any of them. I wouldn't expect much if you go to the actual department stores in Osaka like Hankyu or Hanshin.
Like that very helpful link points out, Joshin is the most useful with its shop-by-shop list of what's in-stock:
Joshin locations: http://goo.gl/maps/0jtxg
Kitamura's web site gives a date of 8 December for the Paperwhite, though it's not clear if that's only for their online shop or if it applies to their brick-&-mortar stores too.
Kitamura locations: http://goo.gl/maps/EVCYT
The K's Denki website comes up blank on a search for Kindle. Not the most convenient locations around Osaka either.
K's Denki locations: http://goo.gl/maps/UKV0X
TSUTAYAs are everywhere, but which ones will stock the Kindle?
TSUTAYA locations: http://goo.gl/maps/91lhl
(Note that the little dots can actually be larger stores than the "A B C" labelled shops on Google's result page -- it seems pretty random which ones they call out)
In Umeda (a central area of Osaka that I'm most familiar with) the most obvious place would have been Yodobashi Camera (if they hadn't explicitly distanced themselves from Amazon) and Sofmap (but I can't find anything about them relating to the Kindle). So your best bet is those four options above.
I hope you can hunt one down while you're here! I ordered mine from Amazon Japan and it should be arriving...soon. Like, today? Or next week? I don't really know...