I came across this interesting article that could allow for a more beneficial method of distributing the federal government nationwide (it already is to a lesser degree with some branch offices), but what Steven Price mentions is that by relocating to a city that better serves its purpose, for example having the Department of Agriculture in St. Louis or Chicago instead of on the coast would be more sensible, not only in some less expensive cities, but to be more accessible to the clients of each department.
Move the federal government out of Washington (Opinion) - CNN.com
So, based on the following cabinet departments as listed below, if Washington, DC decided to break the stronghold with the Feds, where would you move these to? I'm going to list my suggestions, but feel free to include yours, along with divisions of each department (EPA, NIH, FAA, IRS, etc).
State: DC
Treasury: NYC
Defense: Tampa (a possible further breakup for each division though for each of the five main branches though, for example the Air Force in Denver, Army in Louisville, Coast Guard in Hampton Roads, Navy in Baltimore, Marines in San Diego)
Commerce: San Francisco
Labor: Cleveland
Justice: Los Angeles
Agriculture: St. Louis
Interior: Salt Lake City
Housing and Urban Development: Philadelphia
Energy: Houston
Education: Boston
Transportation: Chicago
Veteran's Affairs: San Diego
Postal Service (not a current department, but a former one): Memphis
Of course, the head offices of the three branches (White House, Congress, Supreme Court) will remain in Washington, which could allow for some diversification in the city's economy if handled properly.