On the Shipping Module you can install the "Walk In" option and in the Payment Module you can install the "Cash on Delivery".
If you wanted to disable any other payment but Cash on the website I'm not sure how you would do that. I would assume that it would take a lot of custom coding.
If you wanted to change "Cash on Delivery" to say something like "Cash at Pickup" you can change the tag by following this path: /includes/languages/english/modules/payment/cod.php
But if you do disable any other payment options other than cash if they're picking up...what if a customer from NY is buying something for somebody in your store area and won't be able to pay with Cash?
If you don't want to custom code...you could put in a note on the page that says that if a customer chooses walk in then they have to pay cash (no credit/debit, etc.)
Hope this helps!