Does the idea of the global village mean that certain towns and cities are regarded as global villages?

This is not really what the idea of the global village means.  It does not mean that certain specific locations are global villages while others are not. Instead, it means that globalization has created a situation where essentially every part of the world is closely connected with every other part of the world.  In other words, all the places in the world are part of one global village.

It is true that we can see globalization much more clearly in some parts of the world than in others.  New York City is a hub of global commerce and culture. You can find people from hundreds of countries there on any given day.  By contrast, a small island in the Federated States of Micronesia is not home to the same sort of diverse population and activities as New York.

Even so, we would still say that the island in the FSM is still part of the global village along with New York.  The island has internet and so it is connected to the wider world. The Chinese government is interested in spreading its influence so it has people on the island trying to help with development projects.  People from the island live in the US and send money and culture back.  In all of these ways, even a remote island that most people in the world have never heard of is part of the global village.

So, the idea of the global village does not simply say that some places are globalized and that those places are global villages. Instead, it says that the whole world has become globalized to the point where almost every place on Earth where people live is part of the global village.