"Is she visiting the city?"
Translation:Besøker hun byen?
That would be "Will she be visiting/visit the city?" or "Is she going to be visiting/visit the city?"
What about "Er hun på besøk i byen?" - is that really different? (If it is, my guess is that it means she is visiting someone in this city rather than the city itself.)
Added, however that has the implication that the person is in the town at the moment. The other is asking if she visits the town, and the answer to that can be "multiple times a month" or "rarely", not just at the moment.
But that would then have to be translated into English as "Does she visit the city?", because "Is she visiting ..." implies her doing it at this very moment.
Taking this into account, my translation actually seems to be the more exact one.