Lizzy here, from Shopify support.
Shopify has recently released a local delivery feature built in to the admin! You can enable it under Settings>Shipping.
Your store will be eligible if you have:
There are a few steps you'll want to take first to make sure that your store is eligible and ready. You can read more about those here.
Would that option work for the set up you'd like to have for your business? Feel free to let me know if you have any questions!