Patterns and pattern  matching is probably a nice direction to go.  I
remember having a lot of fun playing with Penrose Tiles at the Maryland
Science Center in Baltimore.  These are really flexible as exhibits.
They are fun to just play with, but are also incredibly interesting (I
spent about half an hour designing my ideal bathroom floor...)
Patterns also occur so often in nature that you can pull in people who are not
really interested in math - point out that seed growth in sunflowers
follows a well-defined mathematical sequence, for ex.  Patterns are also
a part of fractals, which are always really cool.

The other classic component for math exhibits has been topology - but I
get the sense that this has been done to death...

I would go for something to do with music - why a grand piano is the
shape it is, etc.

I would strongly suggest getting in touch with the people at the Maryland
Science Center.  Though they use exhibit ideas that are derived from
previous ones, they put nice spins on them.  Also, you might check out
the booklet that the Exploratorium produced for their "Mathemagica" (?)
exhibit.  I think that's what it was called - done in conjunction with
IBM sometime in the mid 70's.

Kirsten Vanstone
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Kirsten Vanstone
Science Educator
Ontario Science Centre