Frommer's 3-day tour, based on "if you only have one day, do this, and if you have two days, do the day 1 stuff plus this other stuff":
- Day 1: a harbor tour, followed by a tour of Nyhavn (where the tours leave from), the Strøget shopping area and shops in Strædet, a quick tour of the Nationalmuseet (National Museum), ending up at the Tivoli park and fairgrounds
- Day 2: The Wonderful World of Hans Christian Andersen, Rådhus & Astronomical Clock, NY Carlsberg Glyptotek (Carlsberg Collection), the Amalienborgmuseet (Amalienborg Museum), Marmorkirken (Marble Church), the Kunstindustrimuseet (Danish Museum of Art and Design), the nearby Kastellet, and a walk along the Langelinie (where the famous mermaid statue sits).
- Day 3: Museums at Slotsholmen, Ruinerne af Absalons (Absalon’s Ruins), the Danske Jødisk Museum (Danish Jewish Museum) and nearby Den Sorte Diamant (Black Diamond library), the Rundetårn (Round Tower, formerly an observatory built for Tycho Brahe), Rosenborg Slot (Rosenborg Castle), Statens Museum for Kunst (National Gallery).
Note that many museums and attractions are closed on Mondays (fortunately I get in on Saturday). On the other hand, Copenhagen apparently has free bike hires all over the place (with a refundable deposit) so that sounds like a nice way to move about.
Other items of interest: the IMAX Tycho Brahe Planetarium; one of several neighborhood walks or bike rides; the Absolut Ice Bar (kept at -5 degrees C) where the walls, shot glasses, and the bar itself is made of ice; the Copenhagen Casino, which, like all the others I've read about so far, has a dress code and cover charge; the Viking Ship Museum, Roskilde (a half hour train ride out of Copenhagen); and a 35-minute train ride across the water to Malmö, Sweden.
I won't be doing all the museums on their list, but I'd like to hit the Tycho Brahe observatory stuff. I'm sensing the beginning of a theme where I'd like to try to see the space-related places, from Stonehenge to the Royal Observatory in Greenwich to Brahe's place here. We'll see how many other space places I can run into.
But I think two days in Copenhagen followed by a day trip to the Viking Ship Museum and Malmö, Sweden should be enough. That's days 15-17.
To get to Berlin, my next stop, my best bet is an overnight from Malmö leaving at 9:31pm and arriving at 6:04am. Not too keen on getting in that early just because I'm not a morning person, but unless I want to spend an entire day riding the train and stopping in various cities then overnight is probably the best way to go here.