Good to explore alternatives, but I can't imagine ever using a broken axis or a log axis with bars. Bars work by encoding the value as perceived length and both of those treatments (along with non-zero baselines) defeat that encoding.

I don't see that I can include images here, but a couple other alternatives:

1) simple (unexploded) pie chart with two labels, "Inspection Station, $23.75" and "State Fees, $6.25" along with an inset bar chart with the fees.

2) table with a de-emphasized bar chart behind it to add glance-ability