Translation:Is the hospital far from here?
You're right. It could be a/the hospital. Duolingo will probably get back to you in a week or so telling you they now accept your version. That is, if you reported it!
I think in this case we would have to say 'Is there a hospital far from here?' and the question is a bit meaningless because, well, obviously there is. The fact that we ask if it's far suggests we are thinking of a particular hospital, so we must use the definite article. 'Is there a hospital near here?' in contrast is a perfectly natural question (though not 'Is a hospital near here?')