So, in all honesty, I've only been in Malmö for one day in February 2017 and it was my very first time in Sweden. I don't know if that really counts as 'travelling' (don't think so... although I did need my passport to go there...), but I had a really great day, explored a nice city and took some pictures that I believe could be considered worth sharing. From what I've seen, Malmö isn't a large city, but a nice one and it's definitely worth it to spend a day there. Here are some of the places to see/visit that I can recommend:

Malmö Saluhall, which is a nice place to get some breakfast, lunch and/or dinner. It's a food hall, so there is plenty opportunity to try different kinds of food.
The Harbour, for a view of Copenhagen en the Turning Tower.
Folk å Rock, in the centre of the old city. They have nice drinks, cookies and cakes :)
Form/Design Center, to get an impression of Swedish art!
Sankt Petri, a large gothic church constructed in the 14th century. It's very pretty :)
Five O'Clock Tehandel, for when you are a tea-lover like me! Very cute shop.
Malmö City Hall, simply because it's nice to look at. It's really close to the central station, so go there for a quick view of the building and scenery.
Stortorget (main square) and Lilla Torg (little square) in the old part of the city. The scenery in both squares are very nice and it really gives you the 'I am now in Sweden'-feeling.