Here's the route of Old US 99 through Washington:
My last two days of my 1,000 mile bicycle tour of Washington last summer were from just out of Olympia at Millersylvania State Park back to my place in Vancouver. The route I took more or less follows old US 99 the entire way. Now that I-5 has replaced US 99, the old highway is very light when it comes to traffic, with plenty of historical things to see along the way. There's only one 5 mile stretch where the only flat route is along I-5, although it's just from one exit to the next.
Once you get to Vancouver, just take Main street north until you get to Hazel Dell Ave, which is generally a nicer route than Hwy 99. It was once 99 as well. Follow that to the Klineline Bridge, where you'll take a left and head north. This turns into NE 20th Ave, and then NE 15th Ave, which ends at NE 179th. Turn left and go a quarter mile to NE 10th and take a right. Follow 10th and it will take you all of the way to La Center Road. Take a right, and follow this through La Center as it becomes NW Pacific Hwy. This takes you up to Woodland, where you'll take a left onto a bridge into town across the Lewis River. Take a right at the light. In a few blocks, you'll veer left onto Goerig St which then turns into Pacific Hwy, which will take you to Exit 22 on I-5. Here, a nice wide shoulder will lead you to Exit 27, where you'll exit, take a right, and then a left onto Old Pacific Hwy. This goes through Kalam and along the cliffs of Carrolls, giving you some great views of the Columbia. Eventually, you'll have to turn onto Kelso Dr to continue into Kelso, where Grade St will take you into Kelso. From there, it's just a few blocks to Pacific Ave.
From Kelso, you can just follow this route that I took more or less in reverse:
I stayed the night at Sequest State Park, which was about a 5 mile climb from the freeway, but well worth it for the secluded walk-in campsites.
From there, just follow this route in reverse:
I stayed at Millersylvania State Park, which has a few hidden primitive sites that are great for cyclists, but to get to Olympia, you can just stay on Old Hwy 99 which eventually turns into Capitol Blvd as it enters Olympia. Alternatively, Tilley Road will take you right through some of the tall stands of forest surrounding Millersylvania.
I've taken 99 in one form or another all of the way from Eugene, OR to Everett, WA, and I've really enjoyed it. Hope this route works for you.