Done West to East in a Seneca ten years ago. LA to Gulfport Mississipi and back. Plenty to see and do in the Mid west states. New Orleans, Dodge City, Taos, El Paso, Lake Havasu City, Grand Canyon, Las Vegas, LA etc...
Be aware though that some parts of the journey may inlvolve crossing the Rockies, need to check the aircraft performace, also some airfields in the mid west have very high density altitudes like Grand Canyon for example.
Other than that, it's a blast, much easier than trying to go anywhere in the UK. Read the FAR AIM book before you go to get used to the airspace and various regulation differences, oh, and take plenty condoms
