Brownstown is an unincorporated community in Yakima County, Washington, United States. Brownstown is 3 miles west of Harrah. Br…Brownstown is an unincorporated community in Yakima County, Washington, United States. Brownstown is 3 miles west of Harrah. Brownstown has a post office with ZIP code 98920. It is a loosely-knit farming community within the Yakama Nation Reservation approximately halfway between Wapato and White Swan. USPS Post Office for Brownstown is at the intersection of Branch Road with Brownstown Road.