If you do not like your own example, then you may not like this one either, but some of your students might find it interesting. I discovered it along with Roger House when he was an undergraduate.
Let F1 be the 1x1 matrix 1, and create by augmentation 0-1 matrices of larger dimension as follows: (I love < PRE > tags!)
1 1 0 0 ... 0
0
1 1 1 0 0
F_(n+1)= . F_n 0 1 1 0
. 1 1 1 0 1 1
. , so 0 1 is F_2, 0 1 0 1 is F_4, and so on.
Then det(F_n) = fib(n), which is easy. What is a little harder is that you can toggle the bits of F_n to get a 0-1 matrix with determinant k, for any prescribed k with 0 <= k <= fib(n).
Miodrag Zivkovic liked a similar example enough to include it in his paper at http://arXiv.org/abs/math.CO/0511636 . You might check out his paper to see if that example is the sort of thing for your students.
Gerhard "Ask Me About System Design" Paseman, 2010.01.15