First response to jennakalkwarf: I was planning on doing a lot of walking, but to make a long story short, I've recently experience health issues that preclude extensive walking. Just walking inside the attractions will be enough.
Second response to Morten: I've ended up booking HOHO Tours in Tallinn, Helsinki and Stockholm and am now focusing on Copenhagen. I've chosen this approach to enable us to maximize the short time we have in these ports during our cruise (six hours on average).
The HOHO's allow us to first get an overview of the city by taking the whole route, then hopping off at the sites we're interested in. For Copenhagen it's: Glyptotek, Tivoli, Round Tour, SMK National Gallery of DK and Carlsberg Brewery. If time allows, we'd also like to catch the City Tower and the Lejre Land of Legends.
So its a form of transportation to see the town in general, and a way to get the spots we'd like to see.
As I mentioned at the top, we have a full day before and after the cruise. Unfortunately, unlike the other three cities, HOHO in Copenhagen only have 48 hour passes. So we're trying to find a way to get to these sites (over 2 separate days) one day at a time. We're planning on doing it geographically by starting near our hotel near the cruise terminals, the ending at the Central Train Station where our last hotel is located.
That's our thinking and why I'm looking at the Copenhagen Card since they have a calculator on their website that shows how much you save at the attractions provided free with purchase of the card.
Thanks for sharing your thoughts Morten, especially since you seem to be based in Copenhagen!