If you've never been rock climbing, then maybe you can go together. If either of you've gone before and the other hasn't, one can teach the other, or both can take a quick class together. Again, this has to be decided on a case by case basis, different things work for different folks in different times. A bike ride would also work.
I have another reason for suggesting physical activity: the physical state of arousal is about the same for a huge number of activities, such as sex, a fight, being in danger, etc. According to one theory of emotions, we attribute emotions to physical states based on our cognitive assessment of the source of those emotions. So, she and you may then attribute your physiological arousal for arousal for each other. This may not be somin you do on a first date, but its a great way to keep the "fire" burning in a long-term relationship.
You can find research on that here:
Misattribution of Arousal - Wikipedia, the free encyclopedia