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The simplest route for both legs of your journey is to take I-80 between your Midwest points and Akron OH, and then I-76/I-80 between there and Washington. However, to mix things up a bit, you might want to take a different route from Iowa City to Washington, heading southeast from the Quad Cities on I-74 to Indianapolis and then taking I-70 the rest of the way to Washington, or even using I-79 to go south from Washington PA to Morgantown WV and then use I-68. As for places to stop and enjoy some scenery, hiking and swimming, they abound along the Interstates,

AZBuck