This thread got made me wonder, is there a building already set aside for Congress to meet in case the Capitol building is damaged/destroyed? I know the Greenbriar in West Virginia was the Congressional nuclear shelter, but it’s a tourist attraction now.
The Greenbrier facilities are still there, and they could always shoo the tour groups out if they needed it. The Capitol Visitor Center, currently under construction beneath the East Front of the Capitol Building, will have a single large chamber that’s supposed to be used for conferences and such, but is also designed to be useable by either House as a working chamber in a pinch.
The Wikipedia page on the Continuity of Operations Plan of the US government doesn’t mention any significant plan for housing Congress although there is a continual “shadow government” of various executive branch officials in offsite bunkers.
Presumably if the Capitol were unusable, the House and Senate could meet almost anywhere else temporarily, perhaps in a statehouse or even a conference center.
I strongly suspect that there’s another facility below another hotel somewhere, whose existence hasn’t been made public, and this facility is the replacement for Greenbrier.
If the capitol building was destroyed in some non-emergency way (say, it burned down due to outdated wiring) then they’d probably just rent a conference center somewhere in the DC area until they rebuilt the capitol building.
They could always meet at the Metrodome. 
Doesn’t really answer the question, but Congress does not have to meet in the Capitol, as seen by the “Commemorative Joint Meeting” held by members of the House and Senate on September 6, 2002, in Federal Hall in New York City. I do not believe that any business was transacted, just yakkin’.
http://www.gpoaccess.gov/serialset/cdocuments/107-285/text/front.html
It’s a mountain north of the Shenandoah National Park.
I’ve driven by it before. There are signs saying no stopping, etc. Of course, I shouldn’t be saying this; I’ve heard they
There is also “Site R” in Pennsylvania, a completely self-supporting facility built inside of a mountain. I’ve been inside the place and it makes you feel like you’re in a 50s sci-fi movie.