In Forgotten Realms we've always used RAW, which states that (local) works per-region and you can take it independently for each.
It's usually a good idea to ask the DM how likely it is that the party will stay in one region. When the party moves to another region, you can either take knowledge (local) for that region or other skills instead.
I haven't checked how regional RAW dictates, but I would agree with Nuo that requiring a separate skill investment for every region/locale would undermine the usefulness of the skill in a mobile campaign.