In Episode 3 of Real World DC Callie goes out to exercise and ends up running through Lafayette Park and just across the street from the White House.
This would have provided Callie with a pretty good run and the straight line distance from the Real World DC house to Lafayette Park is about 1.2 miles.
Lafayette Square is located directly across from the White House on Pennsylvania Avenue NW between Jackson Place NW and Madison Place NW. Click Here for Google Map showing the location of Location of Lafayette Square across from the White House.
Closest Metro Station: The Farragut West Metro Station and the McPherson Square Metro Station, both on the Blue and Orange Lines, are the nearest stations to Lafayette Park.