Actually, the Vice President lives in the Old Naval Observatory Building in Washington, D.C., at 34th Street and Massachusetts Avenue, a lovely Queen Anne-style Victorian home. No, really.
It was built for the Superintendant of the US Naval Observatory in 1893. In 1929 it became the home of the U.S. Navy's Chief of Naval Operations. Then in 1974 it was designated the official home of the Vice President of the United States, and every VP since that time has lived there. I've driven past it, and it's a pretty unassuming place (albeit large, with a sizeable fenced-in lawn/compound) given that the Vice President lives there -- just a big driveway with a "Naval Observatory" sign.
There are pictures of it, along with some explanatory text (from which I purloined all of the actual facts above) at http://www.whitehouse.gov/WH/EOP/VP_Wife/home.html, which is an "At Home With the Gores" page. Be warned that the rest of it is a bit much:
See their decorating tastes!
Marvel at the Christmas ornaments!
Sigh.