Any phone book has a long list of government offices. So isn't this a silly question?
Not really. All those listed items are departments of government, or representatives of the State, or Town etc. Where and what exactly is the state itself? Like the famous Wendy's ad from 1984, we're interested in the core of the matter: Where's the Beef?
If you want to know where or what is IBM, or any other company or club or church, it's not hard to find out. The phone book may show its head office, or if not any search engine probably will. There will be a place (presently, a government office--but in the coming free society, any physical or on-line service could do it) where shareholders are named and listed. Its annual meeting gives a chance to meet all or some of them. They are real, and they associated in a businesslike way, with a contract stating what are their purposes, what is the limit of its liability, etc.
But the state, or government? Not so easy. It's gray and ephemeral, hidden from plain view. How exactly can we even define it? Louis XIV of France supposedly said "I am the state" because he had centralized control of the country so fully, but that bon mot is remarkable mainly because it's so unusual, less than credible; the state is something separate from any one person, however powerful. More authentic is Louis' deathbed remark: "I depart, but the State shall always remain." So he did really know that the state isn't identical with those who run it.
The best attempt I know is that the state is "the forced absence of a market." But that defines it by a negative! Curiouser and curiouser. Other attempts say government, or the state, is "that which claims a monopoly on initiated force in a specified area" or domain. This is a pretty strange entity, despite its numerous listings in the phone book. And for sure, it has no registered owners or shareholders, though some cynics might point to K Street.
The identity of the state's chief is well known: President, Governor, Mayor, Selectman, etc. But Mayor, etc. of what? What is, precisely, a city? It might be a geographic area, or a set of people living inside its borders, or . . . what? It's no use saying that government is what people elect to perform certain useful tasks, because sometimes government isn't elected at all. In any case, notoriously government does things that ordinary folk cannot do, like forcing A to pay for things desired or needed by B. Election is all very well, but it cannot be a delegation of power, because nemo dat quod non habet -- nobody can give (delegate) what he does not in the first place possess.