Copenhagen in one day?

If possible you should stay two days, and the most enjoyable way that I found to enjoy the city was to just walk, and walk and more walking:))

Use the Citybike system to speed yourself from destination to destination. Unlike the similar system in Paris, these bikes do not require a credit card, only a coin to unlock the latch. However... ... my experience may have been influenced by the fact that I visited in the early spring, but the bikes were few in number and generally in poor working condition. I believe they may release more bicycles in the summer, so perhaps you won't experience the same problems I did. When I could find a usable bike, the system worked great, but it was hit or miss.

We visited in July/August. We stayed 3 days before our cruise and 3 days after but still felt we missed a lot of things we would have like to have seen. One morning was spent visiting Roskilde by train (we purchased 72 hour Copenhagen cards both before and after our cruise that covered transportation and entrances) to visit the Cathedral and Viking Ship Museum. Another day was spent taking the train to Helsingor to visit the castle, then a "private" train further north to spend the day at the beach in Hornbaek. We would have loved to visit Fredericksborg castle in Hillerod, but didn't because the train track was being worked on (so made the trip much longer). We also enjoyed Rosenborg Castle in town, watched the changing of the guard (but didn't tour) at Amelienborg Castle, took a boat tour from Nyhaven, walked the Stroget, visited the museums and city hall downtown, and visited Tivoli Gardens a couple of nights. We could have spent more time and not run out of things to do and see (we didn't even go to Chrisitania, beaches to the south, or across the bridge/ferry into the Swedish side).

As great as the Viking Museum is, with your limited time I'd stay in Copenhagen proper. Musts would include a Canal Tour, Tivoli in the evening, a walking tour through town, Rosenbourg Slot, and maybe a museum that is relevant to your interests - I really liked the Ny Carlsberg Glytpothek but the National Museum was great too. And if the weather is nice, time to lounge waterside at a cafe, of course. To save money, consider a Copenhagen card. You can get one for 24 or 48 hours. If you're trying to see a lot in a short amount of time, it can save you a ton, and you're more likely to pop into things with high admission prices (which is almost everything except free attractions like the NationalMuseet) that otherwise you might not have.

Copenhagen is a fun city, but requires more than one day. Our first visit was just overnight and was just too short a visit. The best way to visit the city is by bus. These are the not to be missed attractions: 1.) Take a cruise around the harbor with a stop at The Little Mermaid that is one of the most popular destinations. 2.) Take a walk down The Stroget which is the first longest walkway in Europe. 3.) Spend an afternoon at Tivoli Gardens and don't forget to stop at some of the presentations like the Chinese Theater. and 4) Spend some time at Nyhaven which used to be a hang out for sailors, but now is filled with great restaurants along the waterfront.