Although I can't say much about Norrköping, having just passed through, I would not want you to miss the ancient rock carvings they have in this city. The rock carvings around Norrköping represent the biggest collection in the world within a city limit. The carvings have been filled in with red paint for easier viewing.
If you're pressed for time, just visit the ones at Himmelstalund to get the idea. Himmelstalund is located right along the E4, the highway to Stockholm. Follow the exit signs to the Tourist Office and Rock Carving Museum.
The picture here is a hunting scene that can be found at Himmelstalund. We placed a pen beside the carving to give it some dimension.