JerseyJoe: You don't state whether you are primarily looking for miles or segments, but if interested in an itinerary along the east coast, would seem you would be concentrating on segments? Also, would assume you could depart from IAD, DCA or BWI on United?
Anyway, my suggestion is that you log onto
www.air-fare.com and see which cities UA might be offering a low fare to from the Washington, DC area. Then go onto itasoftware site and play around with multiple connection routings on those lower cost routes you have found (explanations of how to use the itasoftware site are given elsewhere).
I recently booked a 6-flight intinerary, RDU-PHL, that I located in this manner. Not a whole lot of miles, but getting six segments for $117 to me is a good MR (which is within another MR, COS-RDU). Any time I can average a UA segment for less than $20 I consider that a good run.