Best way to create a property of an association in Drupal 7? I have a node Theater, and a node Movie, and a Theater can have X movies and for each movie at that specific theater there are Y showtimes. How can I set up the property "showtimes" of the association of Theater to Movie within Drupal?
Look into Field Collection:


  Provides a field-collection field, to which any number of fields can
  be attached.
  
  A field collection is internally represented as an entity, which is
  embedded in the host entity. Thus, if desired field collections may be
  viewed and edited separately too.


You can then create:


a content type Movie. You could have fields like a Poster image field, Title, Cast, synopsis, and then a Showtimes field collection.
Then have a content type Theater. Which is a theater. It can have fields like geolocation, a picture of the building, a description, hours of operation, etc.
Then your Showtimes field collection is itself a multi-value field which contains 2 fields: an entityreference to a Theater, and then a multi-value collection of times (maybe look at event module).


Using Views you should be able to list movies, Theaters and their movies, Movies at a certain time -- etc. 

How to integrate this all into the Commerce module or something ... I leave this as an exercise for you.

I don't guarentee this is the best way to build the relationships between data you want. Another alternative to field collection and even the entities could be the Relation module.

EDIT:

If you want to easily create like a Theater that doesn't exist yet for a Movie (when making a movie entry) look at the Inline Entity Form module.