Hi! Investing in some mobility free from scheduled things is what I like to do on a weekend city trip. Kopenhagen especially has a cheap bikes for sale, and you can take them in the train to Malmö and back. Never been in Malmö but in Kopenhagen it's very bicycle friendly. You just don't see enough walking and I never enjoy waiting for busses or figuring out metro charts on a day out. The freedom is fantastic.
Other than that I enjoyed kristiania in Kopenhagen, and hopping from bar to bar none of which disappointed really. Buy your alcohol in Kopenhagen, take it with you to malmo ;) Swedish prices are absurd..
Oh and sweden just passed a ruling that state governed musea are free.