I think the setting of the play, Athens, is really important when you consider the changes that take place within the play between the action that occurs actually in Athens itself, and the action that happens out in the woods.
Athens represents order and education, government and civilization at its finest, and the play begins right in the middle of a dispute regarding Athenian law. If Hermia refuses to marry the man of her father's choosing, he has the right to put her to death. And Duke Theseus is willing to go along with this because it is the law of the land. So Athens represents not only order and law, but also the older generation's unbending desire to uphold said laws.
The woods outside of Athens, where the lovers escape and run wild while having love potion put on the wrong sets of eyes by Puck, represent disorder and chaos, as well as the youthful energy of the younger generation that has fallen into this pastoral setting.
I saw this play recently at our local college theater, and they had tall Greek pillars in the back of a very simplistic stage setting. When the action was happening in Athens, all the pillars were perfectly upright. However, during the scenes in the woods, one of the pillars was tilted about 45 degrees, to represent that things are a bit kooky and off-center in the woods among the fairies!
Check the link below for thematic information about the play!