Apparently ChatGPT Search uses MapBox for local listings. Mapbox said so on LinkedIn & Threads, but OpenAI doesn't mention Mapbox anywhere in their search announcement.

Even though that ChatGPT Search announcement was months ago, there are two recent articles about local search on ChatGPT (Search Engine World, and Local Dialog, which is gated).

Who knows if local search on ChatGPT will take off, but if you want to maximize local visibility you can list your business on Mapbox (if your business doesn't come up in search, click "Contribute" to add it).