If I were trying to charm a young lady via means of music, then I probably would use the piano at all. I may be way off, but I never thought of piano being the most masculine of instruments. Id probably opt for a guitar!
But if thats not an option, then I always find tunes that they recognise. None muso's dont tend to appreciate the finer details of musical performances, so why bother? Play something she knows, and that'll be a good start.
Unless ofcourse she is a lover of classical music. Then you have you're work cut out. Play something romantic yet impressive!