Thanks! Did you enjoy the itinerary overall?
I get to go to Copenhagen on business from time to time. You wouldn't like my "itinerary".
I do really enjoy Denmark, it deserves a stay before and/or after your cruise.
If you can rent a car for just one day (and get moving pretty early in the morning) you can see a couple of great castles and the seaside. Just drive North out of the City, use the road called Strandvejen ("beach road", Rt. 152) which goes along the water with plenty of photo ops all the way up to
Kronborg Castle (be careful, as you approach the castle/town, it's easy to accidentally drive onto road leading to the ferry that goes to Sweden, not that I made that mistake

). After visiting Kronborg Castle, you can find some lunch nearby in
the town of Helsingør or keep moving and drive about 30 minutes southwest on the E47 towards Hillerød (another good spot to find a restaurant) to
Frederiksborg Castle. From there it's only about 45minutes to 1 hour back to the city.
If you want to stay closer to Tivoli, as ldo suggested, there is also the main Scandic Copenhagen. It's a nice part of town, but I always find myself walking towards Nyhavn and the walkplatz that leads from city hall down to the harbor.