To arrive in Monroe by 9 Am on Friday morning is it better to drive 167 to 405 or I5 to 405
One person or more? If more, HOV lanes available on all routes, I believe including 167. Google Maps says about one hour any of three or four routes, don't know if that includes rush hour. I'd tend to stick with the freeways. Check the web for Seattle Area Traffic just before you leave and decide your route then.
Interesting website follows; does not apparently go as far as Monroe, but you might research the site further. http://www.wsdot.com/traffic/Seattle/TravelTimes/reliability/default.aspx
You might consider 18 to I-90, then through Preston, carnation, Duvall road. No traffic that route.
I think this poster has already made the trip.
Going north on 405 to 522 is counter rush hour once you're past Bellevue and much faster. Getting to Bellevue? Faster than 18, especially if you have a passenger and can take the HOV lane.
The road through Carnation is pretty and more relaxing than the freeway, but if you want to make it as short a trip as possible I wouldn't go that way.