Translation:Yes, the castle is popular among tourists.
I think you'll generally find that Buda Castle is capitalized: a Vár as opposed to merely a vár. I suppose it's about like the difference between The White House and the white house.
Yes, "vár" is simply "castle". Each settlement will call its castle "the castle", " a vár", no matter whatever proper name it may have. In Budapest, "a vár" is the "Buda Castle".
You can also think of "the Hill" in the USA.
Are you talking about... Capitol Hill? I'm not sure anyone, myself included, would know what you're talking about if in America you simply referred to "the Hill".
Yes, exactly. But maybe the folks in D.C. are referring to it like that. Not sure. And there may be other hills in other cities. Anyway, the point is, people in Budapest usually refer to the Buda Castle as "a Vár". And there are other towns with castles all over Hungary. So it is each to their own "vár".
To support vvsey's point with an example, in St. Louis "the Hill" would refer to a neighborhood with great italian restaurants south of the city. D.C. would obviously be different...