I am in/through Malmo a few times a year and I can say that it's a boring place on Sunday and thus recommend staying away from there on Sunday. Other days of the week it is fine. A one day trip is nice and if you want you can stay at the Hilton Malmo (but it's quite a hike from the train station). [There are some Scandic hotels there too which can be had for 10,000 HHonors points.] Malmo is not an ultra-vibrant place but a day trip to walk around is nice and pleasant. I remind you of a comment I remember reading about here on FT: "Sweden is boring outside of Stockholm." [I can say I don't necessarily agree with that comment.]

I'll third this option. Louisiana is great, and Malmö is terribly boring.

This is the ticket you mean I think: Around the sound. With that ticket you can also visit the small town Helsingor north of Copenhagen. It is a jovial town nice to walk around in, altough in the weekends it might be full of swedes buying beer.

Just some practical notes:

The train ride from Copenhagen Main to Malmö Central costs 140 dkr return (thats about 19euro). The ride takes 35minutes, and the trains run with 20 min intervals. Route goes past the CPH airport and the fairly new Oresound bridge.
So if you decide to make a Malmö side trip from Copenhagen, its an easy commute.

I find Malmoe a fairly alienated place by Swedish standards. I'd say the most picturesque small town on the Swedish coast facing Denmark is Angelholm. Further afield are the gems of the coastline : Bastad and Tyllosand (a suburb of Halmstad) but both require an hour's additional travel each way.