That's a grest idea, here are some brainstorming ideas for the functionality:

Built-in web? (To reduce size) map overview, based on open street maps:

Functions:

Search location by name

Focus on current location

Enter equipment

At the bottom of the map have a list of locations, sorted by nearest - clicking a location shows an air direction where you have to go, and an option to open the location in the default navigation app so it guides you - a button to navigate next to the location name in the list - to offload navigation capabilities to already existing navigation apps.

Ability to contribute by Adding a PUBLIC calisthenics park, selecting equipment for that location, upload photos (include a guideline on how to take photos - entire park, positioned as where most of the equipment is clearly visible etc)

Ability to confirm already existing locations "confirm park location".

Report a problem (with a list of problems to select from) or inaccurate details, like location, equipment type - maybe edit function, sent for review.

Adding a park scores you some sort of virtual points as a reward.

Some way to contribute these locations to actual Open Street Maps (OSM). Maybe by having all the locations available as a gpx (i think) file in the web version, to be able to be uploaded to OSM.

A check-in functionality is probably useless overexpanding of app functionalit and bad for privacy of users.

Would be fun