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Incorporated, a worldwide network of science museums and related institutions.
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I don't have experience with mats in museums because the only walls I've
seen are low and required no mats.  However as a climber, there are mats
designed for just this purpose.  They also meet two of your three
requirements.  The are durible and easy to replace.  As for cheap, that
depends on your definition I guess.  Climber often use these "crash
mats" is they are going to climb on low rocks with out ropes.  They are
designed to lessen the impact if someone falls from 10-12 feet and not
always landing on their feet.  There are a lot of companies that make
these but Metolius is definately one of the best names in climbing.  I
checked their web site (link below) and the have several different
sizes.  You would probably need a couple of them but they are designed
to take a beating and still work well.  I hope this helps.

http://www.metoliusclimbing.com/crashpads.htm

Cheers,
Woody

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