If you're planning to stay in Malmö and the surrounding area for a little while, you shouldn't miss the opportunity to take a trip to Lund. It's only about 20 minutes away by train, and being the second oldest town in Sweden it is full of history, with a magnificent cathedral, fascinating museums, a famous University, and charming streets, shops and cafes. See my Lund page for more detail.
If you plan to stay in Malmö for a few days, then consider a trip to nearby Lund which is full of history and which is one of Sweden's most famous university and cathedral cities. It only takes 15 minutes by train from Malmö - see my Lund page to read more about Kulturen Open Air Museum and the cathedral astronomical clock.
Lund is University town. It means lots of bycicles everywhere. This is the parking near railway station