First, yes, you inherit a stepped up basis. Your cost basis is the fair market value on the day your mother died. You may need to document this by getting a real estate appraisal, an appraiser can usually do a backdated appraisal based on historical records.
Second, the federal long-term capital gains rate is 15% for most people. New York State and New Jersey do not have special capital gains tax rates, you will be taxed on the gain at the same rate as ordinary income. New York’s income tax rate for most taxpayers is 6.8%, I don’t know New Jersey’s tax rate right now.
Third, if you are a New Jersey resident, you will first prepare a New York nonresident tax return which reports only your New York source income. That would be the sale of the house. Then you will prepare a New Jersey state tax return that reports all your worldwide income and calculates the New Jersey tax on that income. You will get a tax credit in New Jersey for the income tax you paid in New York on the capital gain. In TurboTax, you must prepare the out-of-state tax return first so this credit correctly flows to your residence state tax return.
