Staying home is much cozier (and way cheaper) than going to the movies. But select the DVD carefully. Consider rewatching the first movie you saw as a couple and if that was Dumb and Dumber, then maybe get the first romantic movie you saw as a couple. (On the other hand, in its own way, Dumb and Dumber really is a great love story.) To truly save money, skip the video store or Netflix and take the film out free from your local library which is probably loaded with older movies, though copies are sometimes only available on VHS.
Valentine's Day: A Cheapskate's Gift Guide
How do I love thee? Let me count the pennies