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You can actually set a specific Tax rate by State or Country. But You cannot set up a specific tax rate by City (although you can make use of the State field as your City field). But you will need to have another address field for this.
To do this, just open the wizard on your Auth.net integration. After confirming the details of your account information, on the next page, you will see the tabs to set your Products, Coupons, Shipping, and Tax.
On the Tax setting, you can associate the Address field on your form to set rates for tax purposes.
Hope this gives light to your concern. If you have further questions or you need additional clarification, please let us know.