You will pay taxes to the city in which you work which in your case would be where you deliver the food.
It is also possible that you will also pay taxes to the city in which you live depending on the city. If so, that city will give you a credit for taxes paid to the city in which you worked, however depending on if the tax rate is higher or lower than the one in which you live you may still owe the city in which you live. This is up to the city and how they choose to tax you.
See this RITA fact sheet for more information.
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