I think a cool way to visualize matrix multiplication would be to put three matrices MxN, NxK, MxK on the sides of a three-dimensional box MxNxK. Each cell of the matrix MxK would cast a "shadow" onto some row in the MxN matrix and some column in the NxK matrix, whose dot product would give the value of that cell.
Would you mind elaborating or providing a link for the uninitiated? I use matrix multiplication in almost everything I do and that sounds like a neat way to visualize what is happening.
