From your store's Dashboard, click the Settings icon in the left Navigation Menu.
Once on the Settings Page, click Shipping in the top menu.
Locate the "Price Based Rates" section and click the existing price range where you want to create your Local Delivery option. In our case, we want to offer it as an option to all price ranges, so we clicked the $0.00-Maximum range. When your existing methods are presented, click the Add Method button to begin creating your Local Delivery method.
In the provided fields add the name for your new method (we called ours "Local Delivery"). In the Est. Delivery Time field, add a note explaining the range of your Local Delivery (we specified "Austin Area Only" in ours). Additionally add a price for your Local Delivery method in the corresponding field.
Click the Edit (pencil) icon under Ship To. Expand your Region/Country and uncheck every state EXCEPT the state your business is located in. (Texas in our example). When you are done, click the Done Editing button in the "Edit Ship To Locations" box.
Click the Done Editing button on the Edit Price Rate section to save your new Shipping Method.
Click the Save button at the top left of the Shipping Page to complete the process.
Upon completion, your customers will now see a Local Delivery option in addition to your other existing rates if they are in the same state as your store.