The above poster seems to work for the Reagan Building Parking garage, given their user name. And while there is a fine line between information and advertising, I believe their post crosses it. The Reagan Building is nearest to *PART* of the Mall and *SOME* of the Smithsonian Museums (notably American History and Natural History). But if you are going to the National Gallery or Air & Space other garages are closer.
The RR garage probably is the biggest in D.C. (although I question whether Union Station is larger, for example), but it is NOT the closest to the White House -- the garages along 15th Street north of E Street and along H Street are going to be closer. Whether it is the safest and most secured is also debatable, although I'll concede it is quite secured as you have to go through a security checkpoint to park as it is under government offices.
The RR garage is a good solution for many visitors to many sites, and is frequently recommended. But lets not oversell it as the perfect solution for the entire Mall / Smithsonian area.