I can see evening movies at matinee prices. The discount ticket actually resembles a special pass. So, my coupon-shunning girlfriend doesn't get embarassed when I whip them out. You don't say where you live but a little creativity can adapt them to your location. Pack a picnic and meet your sweetie there for lunch on the grounds.
Many museums have programs tailored to reach children and families for free or at low cost.
If you have the money, a year's membership is a great investment for both you and the museum. As examples, we have a Science Museum, a Children's Museum, the Landscape Arboratum and several zoos. Call and see if they have free days or days when rates are cheaper. Personally, I love the city zoo, which is free and is a great source of drawing subjects. I go there regularly to sketch an old tiger who obligingly sleeps through his modeling session.