Mainly using rails and the occasional airplane.
Along the route of Seattle, San Francisco to Los Angeles, then El Paso, then to Houston, New Orleans, St. Louis, Chicago, Cincinnati, Washington, Philadelphia, NYC, and finally Boston.
I’m using this for an individual story.
How rich is your character? Because air travel was still quite expensive in 1945 -- unless they are very rich or very important (politican, CEO, general), they are taking a sleeper train, which takes between 4-6 days. Also, why are they going from Seattle down to Los Angeles. In 1945 Great Northern Railway was operating the *Empire Builder* from Seattle to Chicago. If you were departing from Seattle, you would probably take a sleeper to Chicago, then there were a couple of different ways to take train from Chicago to Boston.