I shoot RAW and set white balance later, but I find that auto WB gets close most of the time. The cameras I've used (D200, D7000, D810) seem to be clever at recognizing my intent, neutralizing colour casts in daylight or similar broad-spectrum lighting, but keeping the orange of a sunset or the neon green or purple wash of a street scene. One exception is scenes that contain bright snow and ice, which auto WB often renders too blue for my taste. I correct these by adjusting WB until the top edge of the "colors" histogram shows neutral grey (neither blue nor yellow). This sets the brightest snow to a crisp neutral white.
+ 1 for Anthony's advice - when processing RAW images turn the saturation slider up to 100%, adjust the WB sliders to neutralize greys and whites, then turn saturation back down to a reasonable level. I find this method useful for setting green-magenta balance, which I often can't see well at normal saturation.
Cheers - John