I'm so glad you asked that question, Riding the perimeter of the US is my dream. My wife and I did a cross country trip from Los Angeles to Washington DC in 1977. FYA see the website of the Perimeter Bicycling Association of America that records rides (not necessarily world records) around various geographic and political entities, with a special listing of USA perimeter rides:

http://www.pbaa.com/Records/WorldRecords.htm

One entrant, Jane Schnell, wrote a book about her trip:

http://www.amazon.com/Changing-Gears.../dp/0962611204

From the Amazon website:

"On her retirement from the CIA, the author and a companion, Bea, set out to travel the perimeter of the U.S. by bicycle, starting west from Detroit in July, 1986. When Bea gave up in Tucson, Ariz., Schnell continued the journey alone, at 57 becoming the oldest person and the only woman to make the 12,000-mile tour. Bicycling for eight and one-half months of the 13-month trip, she camped, stayed in motels and with friends, took side excursions and accepted an occasional ride. Her journal is a lively record of life on the road--encounters with helpful people, observations of wild animals, weather and scenery. Becoming a connoisseur of local bakeries, Schnell gives them cream-puff ratings from California to Maine. In addition to the satisfaction of completing the tour, she discovered a fresh appreciation of her native land. Photos.
Copyright 1990 Reed Business Information, Inc."

My own definition of the perimeter ride is to stay within a specified distance, about 50 to 100 miles of the border. I have read that among motorcyclists a definition is to ride to each of the towns at the farthest four corners of the country. By this definition one could avoid certain parts of the country, e.g. Michigan, Cape Cod, the Delmarva peninsula, and the southern part of Texas.