After lunch you can feel free to grab a coffee, dessert around the same area. So do some research on the place before going. I know some cafes offer class to let couple learns about small terrarium. It's an interesting thing to do and I am sure you will have a lot of interaction with her.

Usually sightseeing is good as some suggested going to the zoo, aquarium and street art. You can even rent O-bikes to cycle around the street arts area. If she is someone who happens to like sports, you can go hiking, swimming, or bowling (make sure she doesn't have any manicure on).