Tiling and symmetry! You could start with the wallpaper groups, maybe have a station where people learn to recognize and name them (I guess using Conway's orbifold notation or something similar). The great thing about this is that there are beautiful examples throughout history to use. Then move on to the crystallographic groups and explain the application to chemistry; again a lot of nice pictures here. Finally maybe something about hyperbolic tilings, explaining all those Escher drawings.
Related: a guided tour through the proof of the classification of Platonic solids. Conway, Burgiel, and Goodman-Strauss's The Symmetries of Things might be a good place to look for inspiration, as well as Mumford, Series, and Wright's Indra's Pearls for branching out to more exotic groups (although I hesitate to suggest that you do anything about fractals because they already have a disproportionate grip on the public imagination).