The greenest entertainment, of course, is theater -- especially when said theater takes in only the basics, like the table, two chairs, and two-script set-up for Love Letters, or the minimalist classic that is Our Town. But thinking of Our Town, there's a movie that springs to mind -- Dogville. In 2003, Lars Von Trier grabbed Nicole Kidman, and put her through a chalk outline hell in a small Colorado town where there were no walls and no large sets -- just antique props and chalk outlines on the floor. As far as cinema goes, it's tough to get more green than that.
In a similar vein, there are the films that make use of what's already there, and prefer to sit, barely moving, with no fancy shots and only a location or two. Louis Malle's My Dinner with Andre does just that, following a conversation as Richard Linklater would years later, but with even less travel and cinematic fanciness. Dude goes to dinner, sits, and chats with his friend.
Obviously, to go green you have to go indie minimalist. Mainstream Hollywood is too enamored with epic scenery and cinema to ever get very green at all (save the green of Darby O'Gill). So, keeping all of this in mind, what's your favorite "green" movie?