Final answer:
The information provided does not contain details about Philomena and Martin's travels. In the story of Philomena Lee, depicted in the film 'Philomena', she travels to Washington, D.C. to search for her son.
Step-by-step explanation:
The question seems to be referencing the real-life individuals Philomena Lee and Martin Sixsmith, who are central to the story depicted in the film 'Philomena.' However, the provided information does not directly pertain to Philomena and Martin's travels.
The excerpts instead discuss historical events regarding the Underground Railroad and civil rights movement, as well as an incident involving two young girls at a checkpoint, presumably related to immigration or border control.
Without further context, it is challenging to identify the exact U.S. state Philomena and Martin travel to, as it is not mentioned within the provided information. However, as per the narrative of the film 'Philomena,' which is based on true events, Philomena Lee travels from Ireland to the United States to search for her son, where part of her journey takes her to Washington, D.C.