There isn’t a REST API to download just locations, but it is possible to download a MVFv3 file (Mappedin Venue Format v3) that contains the location information. You can read about this here: MVF Locations | Mappedin
If you wish to do so, please contact Mappedin Support to request an appropriate API key and secret to do so using this form: Mappedin | Contact us
You can get the locations from Mappedin JS as well. Read our Enterprise Data Guide for instructions on how to do that.