There are no health concerns specific to Conakry though mosquitoes are more common here than in much of the rest of the country and the general filth of the city means it's wise to pay attention to what you eat. Don't drink untreated tap water.
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Most medical facilities are pretty basic. If something is seriously wrong get yourself to Dakar or home. There are some well-stocked pharmacies along Ave de la République.
Clinique Pasteur Fairly good for malaria tests and minor injuries.
Hôpital Ambrose Paré Considered the best in Guinea, though for anything really serious it's still best to get evacuated out of the country.