Consider:
perhaps mid-May to mid-August; better chance of snow being gone from some of the higher passes, earlier in the ride.
Albuquerque - Santa Fe - Taos -Chama - Durango - Moab. Mesa Verde, Arches, Canyonlands NPs.
Rock Springs, Jackson Hole, Bozeman. Grand Tetons, Yellowstone NPs.
Helena, East Glacier, Whitefish, Sandpoint (Idaho). Glacier NP, including descent of west side of Going-to=the-Sun highway (check for when it will be clear of snow)
Highway 2 west; Grand Coulee, Coulee City, Chelan, Twisp, Anacortes. Grand Coulee Dam, Dry Falls, Lake Chelan (take boat to far end and back), North Cascades NP.
San Juan Islands by ferry (visit Lopez, Orcas and San Juan); ferry to Victoria, BC. See some of Vancouver Island; ferry to Port Angeles; climb to Hurricane Ridge. Highway 101 around the west side of Olympic NP.
South on Washington coast, south on Oregon coast (find the state of Oregon's Pacific Coast bike map).
From Reedsport, inland to Roseburg, up to Crater Lake NP and ride around the lake. Then back to Roseburg and west to the coast at Bandon. (the ride around Crater Lake will be worth it!)
Then south along the Coast.