Dunkers Kulturhus Dunker's Culture House (http://www.dunkerskulturh...) is much more than a museum. Here you can listen to various concerts and experience art, history and crafts. You can also have lunch at the restaurant on site.
It's relaxing to take a stroll around the harbour.
Tropikariet (http://www.tropikariet.com/) Hävertgatan 21, close to Fredriksdal is a small but interesting zoo. Some of the animals are not enclosed in cages but live among the visitors, creating an intimate feeling. The little bird that walks slowly but intently, step by step, in the same lane where the customers are supposed to walk is a little scary, though.
The Tivoli (http://www.thetivoli.nu/) by the sea offers good concerts with internationally and nationally known bands.
"Tura" is a Swedish expression for the local tradition of having dinner on the ferries Scandlines. During summer and the weeks leading up to Christmas you should make reservations in advance. Quite possibly the most classic of Helsingborgian experiences.