Caveat Emptor! Be careful of buying properties on the cheap without checking on the real estate taxes.
Protests to achieve reductions in the real estate tax assessments must be made well in advance of the tax bills. That is to give the Tax Assessor time to hold hearings and determine if assessment reductions should be made or if exemptions and abatements should be calculated. If you are buying a Nassau property in May 2015 you cannot file for assessment reduction until January 2016. That complaint is for the 2017/18 taxes. The first tax bill will be October 2017. That is almost 2-1/2 years after your purchase and possibly a much lower tax would be appropriate based on the reduced purchase price.
The Suffolk real estate tax situation is similar but the period to file a grievance is in May. Village tax complaints to reduce taxes are filed in various months and are usually based on different assessments.