I've done a lot of digging and it seems that this feature is unavailable, although requests date back to 2008. @shopify, is there a reason you've not yet implemented this feature?
Are there any workarounds out there - editing the code in theme directly for example? Which template or snippet would I even find this line of code to edit?
Can radio buttons be used instead of a dropdown?
Any help would be appreciated as I'm having the same issue as tons of others have when users see FREE shipping for local pickup as the default option and don't realize there are other shipping rates to select from.
As shipping options are only presented on the central checkout.shopify.com server, there is no way to customize the order in which they appear-- they will always be presented in ascending order of price. It's possible that there might be a CSS workaround that can be applied to your checkout.css.liquid that someone may suggest, but I would strongly advise not doing this as it can cause unforeseen issues with your checkout.
What I can suggest is applying a checkout translation via your Settings>Checkout Menu. You can simply reword the "Shipping Method" line to include a specification that local pickup is only available within your area so it's perfectly clear that customers must select another shipping method if they want their order shipped.
Let me know what you think!