Possibly somebody else will be able to help you, but I'm going to have to say that in nearly a decade of living here I haven't really found anything really mind blowing in terms of candy. Which is not to say that Japanese sweets aren't amazing - do a google image search of "wagashi". The problem is that these aren't candies and they don't really travel that well. You pretty much have to come to Japan to try them.
When I was living in Canada I managed to find some things. For example daifuku (mochi rice with sweet bean paste inside) is amazing (I especially like goma daifuku, which is unfortunately not popular where I live). Manju (steamed buns with sweet bean paste, etc inside) can probably be frozen and shipped. But it's just not really that good when not fresh.
For actual candy that's available almost everywhere: Pocky is nice -- not exactly mind blowing, like I said, but pleasant. Where I live "matcha chocolate" is popular and worth trying. It's basically coco butter with ground green tea in it. There are even various versions of Kitkat with green tea flavours. Actually Kitkat flavours are pretty crazy in Japan -- some of them are even good. My town is a test centre for Kitkat, so I get to try all of them (as well as Coca Cola -- Peach Coca Cola is horrible, just in case it makes it out of here).
Basically, as far as I know (and would be glad to be proven wrong) Japan doesn't really have a long history of candy making, so the candy you are likely to find is basically just variants of candy that came from other places. There are some exceptions, but I can't imagine the traditional candies I've had being particularly popular for anything other than nostalgia (for example pressed soy bean sugar).