What I think everyone who goes to Malmö should do is go to the seaside. Either the beach and jetties of famous Ribersborg (picture) or a walk in the shadow of the Öresund Bridge at Sibbarp further out. North of Sibbarp is Limhamn marina with its yachts and the yacht club restaurant if you fancy a sit down after your walk. If scenic walking is not what you're after, then visit one of the many art galleries or museums in town. There are also plenty of little design shops in the city centre. Finally, KB, Slagthuset and Hipp are well-known throughout Sweden for their various rock concerts and shows.
Fondest memory: I like to be in a city which is well-organised and full of water like the rest of Sweden, yet close enough to the rest of Europe to feel very un-Swedish at times.
When coming to Malmö you must see the bridge between Malmö and Copenhagen. This bridge has been planned since the 1960's but was just recently built. It not only connects Sweden to Denmark, but it is also very beautiful to look at, especially at night.
Fondest memory: What I miss the most, not living in my lovely home town anymore, is the ocean and the beach parties. We have a wonderful beach on the west coast of Malmö, and every summer people flock to the beach to grill themselves during the day and party during the night. As you walk down the beach you'll hear the waves role in and see dussins of open fires where people are having a barbeque and a drink with some friends. People in Malmö are very friendly and if you are a tourist walking down you are sure to be stopped and talked to. You see men in Malmö are real gentlemen and would like tourists, especially female tourists, to feel at home during their holiday in Malmö. :-)