All National Park Service Areas are off limits without permission.
Rock Creek Park continues to be a difficult area to pinpoint at times. Watch for it carefully. There is a map linked from the NPS page right above the Quick Links. Do not trust Google or Mapquest completely. If in doubt, require that the cacher gain permission from the NPS. The NPS has been annexing areas around the park.
Use caution and be aware of these areas:
The area west of the White House is a MAJOR area to be careful about.
The State Department between E Street to the north and Constitution to the south and between 23rd and 21st street (heavily guarded).
The Department of the Interior is between 19th and 18th street.
Between them is Kelly Park (not NPS), but a cache there failed because that park is watched by the State Department. Just avoid it period.
Moving to the east and working around The Mall...
The IRS Building is on the north side of Constitution between 10th and 12th.
The Department of Justice is just east of that between 9th and 10th.
The FBI Complex is directly north of the Dept. of Justice.
The Library of Congress and the US Supreme Court are just east of (behind) the Capital Dome, east side of The Mall.
Just southeast of the the Washington Monument area is the US Mint complex (US Bureau of Engraving and Printing).
And last but NOT LEAST...
I found a new mapping site that gives the building names for most buildings in DC. Start here with the Washington Monument, then zoom in and out and scroll around as needed. Highly detailed and impressive.
And way to the east of the downtown area, but inside the Beltway still...
The US National Arboretum is cache friendly, but make sure the user has permission.