We did this trip last August (2018). We started in Amsterdam, so had to fly to Copenhagen from AMS. There are not too many other countries you can get to via ferry or train without a significant time commitment to get there. For example, we looked into traveling to Copenhagen from Amsterdam via ferry/train. It would have taken 17 hours (from what I remember) vs. a 1 hour flights. We didn't do it, but I think you can ferry to most of the other Scandinavian countries, like Norway. I'm not sure where your cruise is going, so I don't know if that is doubling up on what you are doing on your cruise.
Malmo, Sweden is right across a bridge from Copenhagen and is easily accessible from Copenhagen.
We took the train to Roskilde, Denmark and had a great day learning how to be a Viking at the Viking ship museum. We also took the train to Kronborg Castle in Helsingor (the castle that Hamlet is based on) and had a lot of fun there.