Copenhagen is a medium sized city, by European standards, with a population of around 1.2 million. From the top of the Round Tower it appears to be a city made up of high density living for most of its inhabitants. Though 'high density' doesn't appear to be any higher than 5 floors (or the length of fire hoses in the 1800s as Copenhagen that has suffered in that regard - two separate fires which each burnt about 50% of the city in the 1700 and 1800s.)
It's definitely a walkable city, though there are ample public transport options (including the driverless metro) and at least 50% of the city's populace gets around by bike. Most of the sights are on the east side of the main canal (marked on some maps as lakes, delineated by the bridges that cross the canal). As with any old city, the streets aren't particularly straight but the tourist maps are pretty detailed so it's easy enough to get around. Note though that there aren't maps in the streets as there are in London.
Highlight 1 - The Round Tower
Finished in 1642, the Round Tower houses a ramp most of the way up, making it easier for the then King to ride up the tower on his horses. The paving on the ramp is worn in interesting ways, presumably by the carriage wheels. The last little part of the tower is a very slender spiral staircase and then you come out on top of Copenhagen.
While you're not that high up, given the short buildings that surround the tower, the view stretches out for an age. It was interesting to see the steeply pitched roofs on the houses - I bet normally covered in snow in late January.
Highlight 2 - Changing of the guards
Very low key, compared to Buckingham Palace, the changing of the guards at the Amalienborg was attended by fewer than 30 people and the 'crowd' was managed by 2 friendly policemen. The guards march from one palance to the other, arriving in formation at midday. With no barricades or crowds the guards marched right up to us before executing a sharp turn. A number of the guards disappeared - to do the paperwork no doubt and then they change places around the square.