I thought I'd just give a short plug for Tony Hillerman, since he pasted away a little more than a week ago. This was his last book and I'd recommend the series. In brief, these books feature an older Navajo police lieutenant and a younger police sergeant who solve cases in reservation areas of the southwest tribes in Arizona, New Mexico, Colorado, and Utah. The FBI is responsible for handling felonies like murder and armed robbery, but often do not understand the underlying dynamics of those indian cultures. The two Navajo policemen do and often solve the cases by coming at them from another point of view and a different entry point, like a stolen pot or container of pine sap.
Some of the most satisfying reading for me is to be immersed in a culture very different from my own and following an interesting human dilemma using points of view that blend the familiar human condition with the unique issues associated with a different culture. In his best books, Hillerman pulled it off well. If you want to get a feel for his writing, try some early books, although this one stands alone as a decent mystery.