Burning Man generates traffic that causes more than the usual dust everywhere in BRC, but a lot comes from upwind of BRC.
In the case of full-on all-afternoon whiteouts, it doesn't so much matter where you camp, but it's much less dusty outside 5:30<=>7:00. Sometimes.
In years w/ sufficient late-winter-season rain & snow, enough to either rain hard on most of the playa or flood it from tributaries, the whole playa is less dusty.
Snowmelt comes in via the larger tributaries, mainly the Quinn River, so the east side may have more flooding & a better surface if this is the main source.
Intense summer rains may only affect local areas on the playa.
Intermittent lakes or rain-flooded areas may be blown around by the wind, and the wind isn't always from the SW.
And what everybody else said.