This depends on where you live,... If your town has a river/lake/sea, that's a safe bet. Inviting her at your place for a movie might not be a stretch, depending on your culture.
If there are public transports, and it's within your reach, you might also consider going outside of town. If both of you have bikes, it's even easier.
Basically you want to spend some time with her, so just find an interesting spot in town (and you know better your town than us). That could be museum's or city hall's gardens, even the local market would do, or simply walking around pedestrian streets.