What should I see in Copenhagen? And is the Copenhagen card worth it?

[RustyBear]

DH is going to a conference in Copenhagen in mid-March & I'm going with him. I'll be on my own for three days while he's at the conference, though we might have time to do stuff together the afternoon before the conference & the morning after, as we fly in early morning Monday and out late afternoon Friday.

The hotel where the conference is being held is very close to the Planetarium, so I'll probably do that; what else is a must-see? (I'm particularly interested in history)

Also, is the Copenhagen card, which covers lots of venues and public transport worth while? I can get one for two, three or five days.

We loved the Torevehallerne indoor food market.

Cocks and cows did a great burger!

Not sure about transport but it’s a very flat city so we walked everywhere

I liked the Copenhagen Card for the convenience of not having to get in line to buy tickets anywhere, but if you aren't an ardent sight-seer and you aren't there in the middle of summer (like I was), it might not make sense financially. You're staying so centrally, and Copenhagen is such an easy walking city that I don't imagine you'll need the transportation benefits of the card.

As a history fan myself, I really enjoyed the National Museum of Denmark, the Design Museum, and Rosenborg Castle, all right in town. The Ny Carlsberg Glyptotek was lovely too. I also thoroughly enjoyed the Bakkehusmuseet, a very atmospheric house museum from the Danish Golden Age, but that might be a bit too far-flung for some. (My family was staying in Frederiksberg, ad we were able to just walk there.)

Have fun -- I am jealous...

Be sure to get a cinnamon bun from the Sankt Peders Cafe!

We really enjoyed a food and walking tour in Copenhagen a couple of summers ago - saw some of the city we wouldn’t have done & ate some interesting food.

Tivoli Gardens!!! Absolute must see and so fun. They were beautiful when we went at Christmas.

Also recommend all the castles and palaces. We did a good tour which was excellent too.

Definitely go to Tivoli gardens together one evening.
Take a canal cruise. Choose one which goes to the Little Mermaid statue.
Walk along Nyhaven. The House of Amber is a lovely small museum and Amber gallery at the top of Nyhaven. It’s open until 8pm, so a good way to fill an evening. It’s on the Copenhagen card.
Wander through Christiania. If you’re going on your own, go early in the morning. Because of the drug activity here it’s a good idea to be aware of the various “do’s and don’ts” before entering.
Factor in plenty of time to visit Torvehallerne Market. It’s busy at lunchtime, but that’s because it has some amazing little places to eat. Lots of it is under glass, so still alright if it rains. It’s a good place for souvenirs and for buying picnics. If the weather’s nice, Id recommend buying lunch there and taking it to the nearby Botanical Garden which is beautiful. It’s also free.
The Carlsberg Brewery has a fun tour, interactive exhibits, horse drawn carriage rides and a showcase of the world’s largest collection of beer bottles. The best part is that admission comes with complimentary beer! I tried a raspberry beer which was delicious. It’s free with the Copenhagen Card.
I’d also recommend going to the Coffee Lab.

Thank you so much for all the suggestions - there should be enough here to keep me busy!

Absolutely go to Tivoli Gardens!

We also went at Christmas a few years ago , Tivoli gardens were excellent as was the boat trip .

Got here at lunchtime and DH and I went out for a walk this afternoon - went to Sankt Peders Cafe - you were right about the cinnamon buns, @NoBarbaraGood - they were lovely. We went to the Torevehallerne market and back to the hotel via a very nice park and along a path by a lake. Tomorrow when DH is at his conference, I will go to Tivoli Garden to pick up my Copenhagen card and take a look at some of the city centre stuff. Today was lovely sunshine, though cold, but there's a possibility of snow/sleet/rain tomorrow, so I might want to keep within range of cover! I might come back to the hotel & go to the Planetarium, which is just over the road.

Copenhagen card definitely worth it if you're planning to see a few sights, also includes the river cruise. Carlsberg factory is worth making the trip out to and card means you can pay quick visits to the palace and museums. It's a wonderful place.

Go to Louisiana , it’s amazing. We stayed near St Peaders Cafe. Round Tower is near there.Loved the boat cruise we did and the bog people at The Museum of Denmark. Wouldn’t bother with the Copenhagen card.

Helsingor is fab - pretty seaside town with Hamet's castle - nice train ride from Copenhagen. We loved the art gallery that looks like a ship - also on the coast, but closer to Copenhagen. Fantastic Damian Hirst collection.

Back home now - Tuesday I did the canal tour - interesting, but very, very cold! Also went to the Amber Museum, got a smorresbrod for lunch, actually in a big department store, as it looked like a good place to warm up. In the afternoon, I went to the Planetarium, which was right opposite our hotel.
Wednesday I got a bus to the zoo - sadly I was just too early to see the giant pandas, which are arriving next month.
Thursday I did the National Museum - at least the Viking & prehistory bits, then went on to the Round Tower and Rosenborg Castle - when I got there I wished I'd gone earlier, as it closed at 3pm - still I did get to do a quick tour and saw the Crown Jewels in the Treasury.
In between I did a lot of wandering around taking pictures, despite the rain.
Unfortunately, I never saw the Tivoli Gardens, except from the outside, as they don't open til April. DH had a conference dinner there, but I wasn't allowed to join him, though he said they didn't really see much of the gardens anyway.
Anyway, it was a great trip, so thanks again everyone for your recommendations!