Now it’s time for your first date! The traditional things like going to movies or at the restaurant, is classical, and therefore not up for completely elimination.
What´s the alternative?
Exhibitions, sports, museums, picnic (which in 2008 was proved to be nice, for 31 % women in the summer). You could also think about pedicure, manicure and something like that, where it would be enjoyable for both of you. You could also arrange to see a movie under more cozy conditions.
The most important is that you both have fun, but you have to make sure that your date knows your wishes and your feeling, so nothing get´s misunderstood.