Choose Local delivery as a shipping method's rate, then list the postal codes it delivers to (a code can be the start of one, such as M5V) and its country. Its fee can be free over an order amount.
A buyer who chooses it enters their postal code at checkout; a code the method does not cover is refused before payment. The method can offer delivery dates on the days of the week you choose, after a number of days and a cutoff time, and the buyer picks one. The date is shown on the order, the buyer's order page, order emails and the CSV export, and Local deliveries in Orders lists the deliveries still to make by date. When the address entered on Stripe's page is outside the postal codes, the order says so.