Helen Margaret Gilkey, born in Montesano, 2 mi away, is the closest. Of the towns next door, Montesano lists the most: 7, with Helen Margaret Gilkey first. The best known of them is Kurt Cobain, with articles in 128 languages. Famous people are on record for 203 of the towns in Washington.
From Wikidata and Wikipedia: people whose birthplace is Brady and whose English Wikipedia article agrees, ranked by how many Wikipedia languages cover each person. Nearby people are those born in a town within 35 miles; distances are town center to town center. People known mainly for crimes, and adult performers, aren’t listed. “The usual town” = everyone born in the towns gathered so far.
Jamie Craighead: United States Air Force Academy, Public domain, Wikimedia Commons
John E. Corbally: Not known. However, given that it shows the president of the university, and was published in the alumni news, and they're announcing the Brundage Scholarships, there is strong indication that it was taken by an employee of or at the direction of th…, Public domain, Wikimedia Commons