Anything by Jaqueline Woodson. She has both picture books (I love "Each Kindness") and chapter books. Anything by Sharon Draper. She writes young adult books more suited for upper middle school and high school. I happened to meet her at a conference a few years ago and she said she started writing because, as an English teacher, she noticed there weren't many books that were representative of her students (diverse population in urban Cincinnati).
A few books with characters or authors who aren't non-hispanic caucasian:
1) "Snowy Day" by Ezra Jack Keats (he's caucasian but the main character isn't.)
2) Illustrator and author LeUyen Pham. we love "Big Sister, Little Sister" by LeUyen Pham (She also illustrates "princess in black" who is caucasian)
3) Spike Lee's "Please, Baby, Please" books
4) Mitsumasa Anno (Japanese artist). We have "Anno's alphabet." Beautiful illustrations. They are out of print but you can find them at used book stores sometimes.
5) Isabella Allende writes books for older kids (City of Beasts, etc.)