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 $F_1$ be the 1x1 matrix $1$, and create by augmentation 0-1 matrices
of larger dimension as follows: (I love < PRE > tags!)
<PRE>
         1 1 0 0 ... 0
         0
         1
F_(n+1)= 0    F_n                         1 1 0 0
         0                                0 1 1 0
         :                   1 1          1 0 1 1
         0             , so  0 1 is F_2,  0 1 0 1 is F_4, and so on. </PRE>

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 $0 \le k \le fib(n)$.

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