Dragor, Open Air Museum, Frederiksborg Castle & Roskide; or Odense, Aarhus & Aero

We did two nights in Odense (about a 90 minute train ride from Copenhagen) and seven nights in Copenhagen, and really liked our division of time (although obviously we wish we could've done even more!). The five days you are in Copenhagen - are you actually staying in Copenhagen, or spending a night or two in northern Zealand? Just asking because if you do Kronborg/Helsingor/the Maritime Museum/Louisiana in one day, it is a very full day (we did it, but we left pretty early and got back to Copenhagen in time for a later dinner).

I am assuming your cruise leaves form Copenhagen. If you have three days, I would consider spending two of them in Odense, and one more in Copenhagen. From Copenhagen, do a day trip to Roskilde (UNESCO World Heritage Site cathedral, absolutely awesome Viking Ship Museum). You could also definitely do a half day trip to Hillerod for its castle. Aarhus is like a 3 hour train ride, which isn't so bad, but if you have just 2-3 extra days, I personally would stick to the things closer to Copenhagen, considering there is so much to do. Also, I don't think you can get a train to Aero. I think you take a train to Odense and switch to a bus, and then a ferry. Would be beautiful no doubt, but sounds like a lot to me given the time you have.

Correction, for Aero, you take the train to Svendborg (with a change in Nyborg, the first stop on the island of Funen), and then a ferry I believe.

First of all use www.rejseplanen.dk to plan all public transport in Denmark.

Generally speaking I would say that Copenhagen itself warrants 3 days at least and then there are the most popular day trips. 1) Helsingør and Louisiana (can be done in a long day). 2) Roskilde. 3) Hillerød and Frederiksborg Castle. Dragør is indeed a nice fishing village alternative to Ærø. It's fairly small, but a nice place for lunch at the harbour and a stroll around. It's 45 minutes by bus from Copenhagen. If you decide to do these day trips, look into the Copenhagen card for discounts on public transport and entrance fees.

Ærø, Odense and Århus are a bit far a way for day trips. Personally I think Odense is overrated, but if you are interested in Hans Christianian Andersen, you could stop by his birthplace and museum in Odense for a few hours on your way to Ærø or Århus.

Thanks for the responses. Can one make a day trip to the Frederiksborg Castle and the Open Air Museum in the same day? What would be the travel arrangements using trains and/or busses? Is a visit to the Open Air museum worth the time? Would the Copenhagen card cover entrance and travel? Is it possible to visit the Frederiksborg Castle and Roskide in one day trip? Would the entrance fees and transportation be covered by the Copenhagen card? How would one travel arrangements using trains and/or busses?

Sure you can visit Frederiksborg and the open air museum on the same day, they are fairly close to each other. The open air museum would not be my top choice, but I have been there many times, so perhaps I am not the best person to ask.
Frederiksborg and Roskilde are only connected by bus and it's quite slow. The travel arrangements can be found on the link I posted above. Transport is included in the Copenhagen card and you can find which entrance fees are included on the cards website http://www.copenhagencard.com/whats-included

Thanks for the information. I believe that we will keep our hotel in Copenhagen as a home base and see sites we would otherwise be unable to see, and we will also plan day trips from there. I will continue reviewing the Copenhagen card to see if it works for us. That information and the travel site is are very helpful.