RE: What would be best way to (1) refund employee the tax withheld?
1. Create a legibility adjustment that is set to not impact account to negate that tax and the wages.
2. Write the employee a standard check using the payroll liability account used on the city tax item.
RE: What would be the best way to (2) amend the records so the locality account payable is reversed and said employee will not appear on future reports for locality in QuickBooks withholdings due to not being locality resident and not working in locality.
Well, Accounts Payable isn't involved in any way in payroll taxes in QB, so not exactly sure about that.
To stop the tax on future checks, remove it from the employee record.