I would say 'Greg and Me.'
Since it isn't a full sentence, a good argument can (as we have seen) be made on both sides.

The caption depends on the intent of the writer, I think.
Are you saying in your head "Greg and I are at the movies."
or "The sky is falling on Greg and me."

When Me or I is alone, it seems a more formal approach to say "I" and more casual to say "me."