I really like the little outfits I see Japanese kids in with the little ears and tail (like a sheep or a bear) every time I've been to Japan. So now I'm pregnant, I want to buy some to take back to US when I'm in Tokyo next month :)
I'm not sure if the stores below have the type of clothes you are looking for (the ones with cute little years and tails), but these are the most famous baby clothes stores that I know of.
Most of the branches are in more residential areas but there is one branch in Odaiba (Decks Odaiba).
Odaiba shop: http://www.24028.jp/tenpo/detail.php?cid=13&doc=827
They have cheap clothes and lots of Japanese moms love to shop at Nishimatsuya! (My friends, too)
Akachanhonpo has not only the clothes but all sorts of babies goods. However, this shop do not have branch in central areas like Nishimatsuya. The closest shop to the central area should be Gotanda TOC branch: http://www.akachan.jp/store/0031/
Shimamura is not specialized in babies or kids clothes, they have womens and mens, too. Many moms love cheap fashion stuffs from Shimamura. I just saw the advertisement of this week and found clothes (cape?) with rabbit ears :)
BabiesRus is in anywhere but this is the place to go for Japanese, too. There is a branch in Ikebukuro Sunshine City shopping mall: http://www2.toysrus.co.jp/store/storeinfo/store.php?id=4761
Of course there are GAP babies and ZARA babies and those are popular as affordable babies clothes for Japanese moms :)