Troubleshooting
The "Deliver to" bar doesn't show. Check that the module is on in Modules. The bar is hidden on the checkout page on purpose.
A distance area never matches. The outlet needs a map pin: edit the outlet and click the map. The outlet list shows No map pin when it's missing. Very new or unusual pincodes may not be found on the map; add them to a pincode-list area instead.
Every pincode says "we don't deliver". Check that the areas and their outlet are Active, and use Test a pincode to see which area (if any) matches.
Local delivery shows the method's old price. Choose that method as the Local delivery method in Delivery settings and click Save. Only the chosen method is priced by your areas.
Shoppers outside my area can still order with a courier. Your setting Shoppers outside every area is "Can order with your other shipping methods". Change it to "Can't order" or "Store pickup only".
A product must never go by courier. Switch on Local delivery only for it in the product editor's Shipping tab.