One of the various ActivityPub Vocabularies that one can post is an "Arrive" verb[1], as in, I arrived at this place. This would work well for a foursquare like check-in system. If you want something more real-time, you could either keep updating the location of that Arrive object, or just keep posting, every time you move more than 10m or whatever.
Sorry that I don't have anything helpful right now to offer! But I thought I'd share, as this is definitely part of the shared, open-standards based social systems that I hope we start to build, use, enjoy, & extend.
[1] https://www.w3.org/TR/activitystreams-vocabulary/#dfn-arrive