Copenhagen's cycling or walking routes start, of course, in the historic city center. There's a beautiful palace complex called Amalienborg (open until 4 p.m.), city hall, the Nyhavn Canal and a huge number of museums (note - they're all closed on Mondays).
Not far away is the wonderful Tivoli Amusement Park. Be sure to include it in your Copenhagen with kids itinerary. A little further on is Strøget, a shopping and pedestrian street.
You don't have to walk in the city, there are bike lanes. While many tourists stubbornly alternate between walking and taking a cab, bicycling is actually more convenient and mobile. Take a look around - the city's residents themselves make a compelling case for cycling.
While you're in the center, take a ride on the river streetcar, which is sure to pull up to the Little Mermaid statue.
Take a visit to Christiania, a Copenhagen neighborhood that has become a haven for informals of all stripes and claims to be an independent state.
When planning your Copenhagen itineraries, don't hesitate to pick up a Copenhagen Card, which lets you visit dozens of the city's most interesting places for free.
The card will also be your pass for transport, including river streetcars and trains, urban and suburban. And with this card, some restaurants will give you a 20% discount. The cost depends on how long it is purchased for.
