So for me, a first date doesn't even have to be in a restaurant.
As a PP said, a movie is out since you can't even talk. But for me, going to the batting cages, go carts, a theme park, some kind of festival, bowling... all sound great to me! No concerts, no museums...
For dinner, I wouldn't really care. If I'm actually into someone I could be doing community service along the highway and it wouldn't matter.