How do I do this with WordPress? Taxonomies?

Three methods:

  1. Don’t use taxonomies at all, just store the ID of the associated posts as post meta
  2. Create a taxonomy, and remove the ability to edit/delete/create terms. Then use automation to catch the hooks for the creation, editing, and deletion of Place posts, and create/edit/delete the associated terms in the taxonomy.
  3. Use the Posts2posts plugin by Scribu, though this would require learning a new API and adding an additional plugin dependency

If your relational mapping is a 1 place can have many events, but one event can only have one place, then a fourth option becomes available:

  • Set the parent post of an event to its place