An apparatus in one embodiment includes at least one processing device comprising a processor coupled to a memory. The at least one processing device is configured to obtain in a host device information characterizing local-remote designations of respective first and second storage systems, one of which is designated as local and one of which is designated as remote, and to adjust path selection in a multi-path layer of the host device based at least in part on the obtained information characterizing the local-remote designations of the respective first and second storage systems. In some embodiments, a given logical storage device is accessible to the multi-path layer of the host device via a first set of paths to the first storage system and a second set of paths to the second storage system, and adjusting path selection in the multi-path layer comprises adjusting weights assigned to respective ones of the paths.