There is no US state without property tax. Maybe you are thinking of income tax (Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington, and Wyoming) or sales tax (Alaska, Delaware, Montana, New Hampshire, and Oregon)?
> Thorne Bay is a Second-Class City within an unorganized borough on Prince of Wales Island.
> Thorne Bay does NOT LEVY PROPERTY TAXES.
> https://thornebay-ak.gov/land/
You get what you pay for as far as services are concerned though.