I imagine in Central NJ you are used to driving your rig on urban freeways. The freeways through the Seattle metro area (Everett to Tacoma) can't any worse than that. But go to the WSDOT website if you need more information on traffic levels and such. I've also gotten good traffic timings from Google maps.
But for these parks you don't need to pass through the cites, provided you are willing to spend some money on ferries.
WA20 or US2 across the eastern half of the state, the WA20 across the North Cascades is a good scenic choice. Then continue on WA 20 onto Whidbey Island, and short ferry ride to Port Townsend (check WSDOT for times, fares and reservations). Check WA state parks for this area.
Then loop around the Olympics (I just did that in 3 days with a 2 night stay at Kalaloch Campground. Use the jeep to take side trips into the Olympic mountains and valleys.
Then US12 to the Rainier area. Camping on US12 around Packwood might be a good idea, with Jeep drives into Rainier, and maybe south to St Helens. The road up to Paradise can be driven in the full rig, but would be more fun in a car - especially if you want to park and takes walks.
You can drive any state and federally numbered highway with your rig (at least in Washington).
