I am not a linguist, but I try to tell: nincs - you say when something isn't. I mean it doesn't exists, or at least doen't exist there, or at that time, etc. So you say nincs, when you negate the being itself. But in the sentence above there IS a bank. You don't negate, you don't deny that there is a bank. You negate only the location of it. So you say "van", and not "nincs" - because there IS a bank. But not there.

He isn't at home - Ő nincs otthon. (the main, that you negate his "being" at home) He isn't at home, and that's all. You don't tell any alternatives, it is enough to tel, that he "nincs" at home.

But when you add that what other place he can be, then you say: Ő nem otthon van, hanem máshol.

Well... I feel it wasn't the best explanation, but at least it is something like that. :)