^I think you downloaded the wrong Utada songs, not all her songs are r'n'b and alot of them are very 'pop'. Try Traveling, Deep River, Final Distance and Hikari.
maybe you want to try
Mika Nakashima or
Kiroro? The first one you should've heard plenty about, she's mainly jazz/acoustic-sounding so they are good to relax to. The second one's less famous here but they were famous in Japan. It's a duo of two girls, one vocals and the other one plays the piano. I'll upload a song or two of theirs soon if you want me to.
other recommendations:
Kou Shibasaki - great voice, she's a famous actress and her songs are very popular in Japan.
ZONE - girl band, a few songs are great.
Ken Hirai - he's supposed to be R'n'B but don't let that turn you off cuz his ballads are great. He also sings in flawless English.
You Hitoto - can't really describe her style...but personally I think she's probably as unique as Shiina Ringo.