I am able to configure my site with items that can only be picked up locally (even though the default design does not state that clearly in the payment screen), and items that will be shipped. But I have a brick & mortar location, and I would like to provide the ability for the customer to select, individually, within the same shopping cart, which items he wants to pickup locally (items that are local pickup only as well as items that he prefers to pickup even though they can be shipped), and which ones he wants to have shipped.
Is there an app that can provide this functionlity?
The exact functionality you're hoping for doesn't exist due to limitations with Shopify's checkout (it's fully locked down), but you can get the same end result using Intuitive Shipping.
There are typically 3 scenarios that happen:
The entire order is shippable (the customer selected items that can all be shipped). The customer can be shown both a shipping option, along with an option for in-store pickup
The entire order is pickup-only (the customer selected items that are pickup only). The customer can only be shown in-store pickup.
The order contains items that can be shipped, along with items that cannot (the customer selected items from both categories). The customer can be shown an option to ship the items that can ship, but pickup the items that cannot. They can also be shown an option to have the entire order picked up in-store.
Using Intuitive Shipping, you can use our robust Conditions engine to assign rules that apply for each of these scenarios and then display the appropriate options depending on the cart combination. It doesn't let the customer cherry-pick the products they want to pick up and ship like you described, but it gets you your desired end result.