Malmo is only 20 minutes from Lund by bus, and the first city as you cross the bridge from Copenhagen to Sweden. It is the third largest city in Sweden with around 300,000.
I wasn't expecting much, which is perhaps why I did not end up visiting until nearly the last month here, but I was pleasantly surprised. They have a well preserved old town, and although it does not match the scale of the one in Stockholm, it is full of very old tiny cottage like houses and cobbled streets.
The most famous attraction is a tall building in the middle of nowhere called the turning torso. Other than that they had some really nice parks filled with tulips, some rivers, waterfronts, a few plazas, and a castle from the 1400s constructed as a stronghold for Denmark when they controlled this area.
Other than that, due to it's location, Malmo has been the first port of entry to Sweden for immigrants, and hosts a large population from Arab countries (Iraq, Iran, & Lebanon mostly), plus Poland. About 30% of the city is immigrants (probably the most of any city in Sweden). That certainly seems to be a point of political contention and media attention nowadays given the slow trend taking place in Europe that seems to be anti-immigratory.
I tried to blend in, guess it didn't work:
Part of Malmo castle with a moat:
Their main train station has videos and slide shows projected on to the wall. No fair: