While she's pretty big in Japan, Sheena Ringo, as well as her band Tokyo Jihen, aren't very well-known outside the country (Doesn't help that a lot of their stuff are blocked on Youtube, although you can find some of her live performances, which are amazing.) Picking only one of her songs is difficult, as she's a rather diverse artist, but I'll go with one of her Tokyo Jihen songs, which is how I got into her:
http://www.jpopsuki.tv/video/Tokyo-Jihen---Noudouteki-Sanpunkan/c15d3170aa4a99293760176bba102317
It's simple and classy. Nothing grand or bombastic, or even weird, just a sweet, groovy tune. It's sorta the band's "Another One Bites the Dust." Sheena Ringo is my favorite singer, as she has a strong, distinctive voice, and is one of the few Japanese artists who can sing very well in English. The other band members are very talented as well.