If you itemize deductions you can deduct the real estate tax on the new home. But your total deduction for state and local taxes is limited to $10,000 ($5,000 if you are married filing separately). The maximum applies to the total of real estate tax, personal property tax, and either state and local income tax or state and local sales tax.
You can also deduct the mortgage interest on a second home. You can only deduct mortgage interest on two homes.
Other than that, buying a second home will not affect your taxes until you sell it.