There is no inheritance tax in NYS. It is an estate tax that follows the federal estate rules. At $439k you will not owe estate tax, you are below the limits under the current law.
Regarding capital gains tax - the estate receives a stepped up basis for the value of the house to the value at the date of death. If you did not sell it for more than that value you will owe no capital gains on the sale of the house.
Is the rest of the estate cash? If that is the case you will owe no income tax on that either.
There is the potential that no tax will be due on any of this money.