Taken literally your question is about post to post relationships. Bad news — WordPress core doesn’t do post to post relationships. However there are some solutions ranging from frameworks like Posts 2 Posts to plugins like Post Connector.
Stepping a bit back though, structure you are describing strongly implies grouping of posts. The mechanism for such in WP is custom taxonomies (core taxonomies being categories and tags for example).
If you create Place and Activity as taxonomies then you get pretty much everything out of the box — from UI in post editor to archives and querying. The only limitation would be just how much info you want to cram into individual place/activity items (terms of taxonomy). They aren’t to be intended as content heavy as posts and many less tools focus on enabling complex data for them.
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