grammatically the support verb should be "would" instead of "will"... future in past.
That would translate to "Você disse que os médicos estariam naquela cidade"
'town' was not allowed
this is an error, you must report
"At that city" should work here, shouldn't it? It was counted as incorrect.
"in" is used for cities, towns and countries. Not "at".
that does not feel ok but I do not know why...
It could be, depending on the context, e.g. if the doctors are moving around and just arriving there.