Hi Arlene, I found the Williams' family in 1880 in Ness Co., Kansas. William Williams, b. VA, 37, farmer. Elvira J., wife, b. VA, 34, temporary disability-childbirth. Francis M., stepson, b. VA, 13. James L., b. VA, 9. Sarah E., b. VA, 8. Mary W., b. VA, 6.
I've never heard of a Washington City Directory for Seattle. Could this be Washington D. C.?
Who is your grandfather and when and where was he born? Maybe I can trace William that way.