Is there a Report that Provides Sales Tax Collected by County?

Unfortunately, we don't have any built-in reports that will outline tax paid based on County. We have sales reports for Sales by State but not to the County level.
If you are using ShipCompliant, we would recommend obtaining this data from their reporting system. 
You can also perform an Order Export and sort the Zip Code column to sort orders based on Zip Code and manually add the values together. There is also a column for City, if you want to look at Sales Tax by City.