If barbecue is not your thing, cook as you usually would, and then set a table out with candles and a rose in a vase, and you are all set for a nice cozy meal. Even two friends or siblings can really have a great time with this idea.
A gourmet dish made with a splash of red wine, pasta, ravioli, or the likes will be just perfect. However, this one is better suited for a romantic evening rather than a dinner setting for a parent and child.
Put up a tent in your yard and have dinner inside. You can play good music in the background. For a more nostalgic evening, go to the place you first met your dining partner. Eat around that place and walk there under the stars. If that place was a restaurant or a cafe, you could simply eat there.
The same thing can be done if you are taking one of your parents or arranging a dinner for them. Ask them where they met for the first time or where they first had dinner together, and make arrangements for a special dinner for the two of them.