The best source of bicycling information for Washington State is the Washington State Department of Transportation - Bicycling website http://www.wsdot.wa.gov/bike/
There is a link specifically for planning tours: : http://www.wsdot.wa.gov/bike/Planning_Maps.htm
There are links to Accommodations, Campgrounds – Washington State Parks, Washington State Ferries and Amtrak Cascades, Bikes on Transit, Bicycling from SeaTac Airport, Bicycle Paths and Trails , Bike Clubs, and Local Bike Shops by County .
I've ridden State Route (SR) 20 in both directions. Either way you have a steep, but georgeous climb. This area is known as the Washington Alps. We were totally spoiled for our 2004 Cross Country Ride during our first week crossing the Cascades! Nothing could compare! The Adventure Cycling Northern Tier Route follows SR 20 (mostly), so Northern Tier Map 1 would help. Although ACA leaves SR 20 at times, there is no real reason to do so, especially since almost all the services are on Highway 20. But, do keep in mind, it's a mountain pass, conditions could be cold, wet and nasty! You are surrounded by National Forest and National Park, so ammenities are limited.
The route along the Methow River on SR 153, and Columbia Rivers on US 97 is very nice. It can be very hot and there are few services. The section between Wenatchee and Leavenworth has more services.
The return route over US 2 is also very scenic. Again, it's National Forest land with few services.
The west side connection between US 2 and SR 20 is the hard part. SR 9 used to be a nice quiet alternative to I-5, but not any more. Last time I was on it (in a car), traffic moved very slowly if at all. There are some alternate roads, which may involve more hills, but could get you away from the traffic.
Try exploring the maps at http://www1.co.snohomish.wa.us/Departments/Public_Works/Divisions/TES/ProgramPlanning/transpelement.htm
for a route between Monroe and Sedro Woolley.
Explore the Snohomish County bicycle club, B.I.K.E.S., http://www.bikesclub.org/
, website. See if you can find someone to contact for information on avoiding SR 9. (Let me know the answer.)
Northwest Mileposts , http://www.amazon.com/exec/obidos/tg/detail/-/1878425803/qid=1114399769/sr=8-1/ref=sr_8_xs_ap_i1_xgl14/002-1457820-3881626?v=glance&s=books&n=507846
, last published in 1995 has mile-by-mile logs of SR 20, US 97, and US2. Although 10 years old, the descriptions for National Forest and National Parks areas haven't changed much.
In case you decide you don't want to carry your gear, Adventure Cycling has a supported loop tour of the north cascades and more http://www.adventurecycling.org/tours/cyclewashington.cfm?pg=more
. (Jul 30 - Aug 08; Route begins and ends in Redmond, WA; 10-day catered and van supported event, 10 days, Miles: 50 Daily average Roads: 100% paved Riders: 150 Cost: $999
CycleAmerica does a North Cascades Loop: http://www.cycleamerica.com/np11cascades.htm
(August 13 - 19, 7 days, $645).
Have a good trip!