My suggestion for an ideal domestic trip is in the Pacific Northwest. Late summer is the best weather, yet cooler than many parts of the US. It isn't likely you'll suffer from the heat.
Trip 1: Start in Bellingham, Washington, down Chuckanut Drive, over to the San Juan Islands for a week, then to Port Townsend and down US 101 on the west side of Hood Canal, then duck over to the coast, pick up 101 again and ride it south to Brookings, Oregon. The down side of this trip is that it does start and end away from major airports although you can rent and drop off cars or U-Hauls, or dog it (Greyhound). Bellingham is 90 minutes north of Seattle (Amtrak goes there too), Brookings is 2 hours from Medford which has a major airport, or even San Francisco.
Or start in Seattle: north to Mukliteo and cross over to Whidbey Island, go north to Anacortes and the San Juans--again for a week, then to Victoria and Vancouver Island, back across the Straits of Juan de Fuca to Port Angeles (Hurricane Ridge at Olympic Nat'l Park!), Sequim, Port Townsend, then to Kingston, then Seattle. It does a loop from a major city so transportation in and out isn't an issue.
Or mix it--Seattle, Bellingham, Victoria, San Juans, Seattle--the possibilites are numerous.
Whatever you do, keep us posted!
John in Oregon