I want to preface this response with a note that I am not a property tax expert nor an attorney. This response is based on my experience as a real estate agent on the North Shore
Property taxes in the North Shore (Cook County) suburbs generally run at around 2% of the genuine market value or slightly less. One would think that the property taxes should adjust to a level around $14,000. Of course, the formula utilized to compute property taxes is much more complicated with the most important factor being the "total assessed value" which is determined by the Cook County Assessor. Many homes that have not had a transaction in recent years have an assessed value that is considerably higher than the current value.
There is a very specific process by which a homeowner can protest their property taxes. This can be found at :
Having a recent "arms length" transaction of a non-distressed (foreclosure or short sale) property is a very strong tool for waging a protest. Many homeowners have had success protesting their taxes.
Many North Shore residents hire attorneys to protest their taxes. These attorneys are generally compensated based on a percentage of the amount of money that they save you and often receive no compensation if they are unsuccessful.
Tearing down a garage?...Maybe, but probably not significant.