Your US tax liability will depend on how you gift the property.
If you own the property when it is sold, then you may have a taxable transaction because you are still the owner. However, the value (cost basis) of inherited property is the fair market value on date of death, so there may be no federal income tax due if the property has not increased in value.
You may have to file a gift tax return (see below).
Is money received from the sale of inherited property considered taxable income?
If you transfer ownership to your niece prior to the sale, then there is no US income tax because you don’t own the property, it’s located in Hungary and your niece is not a US citizen or resident.
If the value of the property is more than $16,000 you would have to file a gift tax return. You would not have to pay any tax. You simply show that your lifetime exclusion is being reduced.
TurboTax has an excellent article on The Gift Tax. TurboTax does not have software to prepare a gift tax return. This is a complex return so I suggest hiring a tax lawyer or accountant to prepare this form.
