I don't believe it's possible to customize the checkout page that way, though I would recommend contacting Shopify support to verify that.
Alternatively, Intuitive Shipping lets you set up sub-zones in your Shopify Shipping Zones using postal codes. We've found it's a common need in places like the UK where Shopify doesn't offer Zones for individual UK countries and regions. So as an alternative to using cities, you can create a Condition Group with a range of postal codes and name it accordingly, then apply it as a rule to a Shipping Scenario to either exclude or include shipping in that zone.
Or, you can simply set up a Scenario with a City Condition and add as many cities as you need, separated by commas. The outcome is similar to using postal codes, though postal codes will cover more territory.
Either process will limit shipping from being offered in these areas, so if a customer isn't eligible, they'll get a cart failure. If you want the customer to know in advance if shipping is available in their country/city/postal code, you may want to consider pairing this with an app that verifies the customer's address before they move to checkout.
If you'd like to learn more about Intuitive Shipping, please feel free to book an appointment for a demo with one of our team members. You can install Intuitive Shipping for free and use it in Testing Mode as long as you need to see if it's a good fit.