1. There are bikes. Lots of them.
It isn't car traffic you need to look out for in Copenhagen. About a third of all citizens in Copenhagen commute to work, school or University. In fact it is said that more people commute by bike in Copenhagen than in the entire USA. It certainly is one of the most cyclist friendly cities; although because of this perhaps the same can't be said for pedestrians. There are dedicated bike lanes, however I nearly got wiped out by cyclists on several occasions, as they appear to come from nowhere at times. Be warned...
2. The metro trains drive themselves.
In Britain this would cause strikes. In Denmark they just use logic. The trains are completely automated, stopping at each station just like any other metro system. No need to have a human doing it. I hopped on at the airport and arrived at the city centre in minutes.There are even large windows at the front and back, allowing action-movie-esque views as the train speeds through the tunnels. Cool.
3. It's expensive.
But not if you are organised. If you do some research there are plenty of places to eat that are less expensive, particularly to the West of the city. Also there are many places you can enjoy for free, such as Kastellet, a fantastic fortress with a beautiful windmill, and of course the statue of The Little Mermaid.
4. It's small.
Which is great, because if you are only planning on visiting the centre, you can pack a lot in to just one day. Most of the main attractions are within walking distance of each other. Despite the aforementioned bikes of doom, it is practical and quick to walk around and soak up the sites.
5. It's super connected.
If you wanted to explore further into Europe, Copenhagen is a good starting point. The Oresund bridge links Copenhagen directly to Malmo in Sweden, which could easily be done in a day. The superb rail links also make Norway, the Netherlands, Finland, and just about anywhere in Europe within easy reach. Of course the rail links within Denmark itself are also superb, with modern, frequent trains, putting the rail network in Britain to shame.