The CPHCARD gives you free entry to 60 museums and attractions, free transport by train, bus and subway - including to and from the airport - and discounts on some restaurants and sights.

The card must be ordered before your trip, as it cannot be purchased once you are here; details at http://tinyurl.com/m76qag.

The heart of Copenhagen is small and most sights are within walking distance. One way to explore the city is to do like Danes . . . on two-wheelers. Danes are eager cyclists and there are 190 miles of bicycle paths in Copenhagen.

Several shops rent bikes all year round from $15 (75 kroner) a day. And from mid-April to November, there are free bicycles around the city. To get one, insert a 20-kroner coin - which costs about $3.80 - to unlock a bicycle rack, the same way travelers get luggage carts at airports. Bicyclists get the coin back when they return the Bycykel - Danish for city bike - to the racks.

The city also has a well-functioning transit system, though the fare is steep, at $4 (21 kroner). But buy a 10-ride card at $25 (130 kroner) and each trip will then cost you $2.50 (13 kroner).

In 2009, the City Cirkel line was launched, providing small environment-friendly, yellow buses that drive every seventh minute near the main sights for the price of a regular ride. They're much cheaper than the sightseeing buses that tour the capital.

The public transportation operator also has a so-called "harbor bus" that zigzags through the harbor. A ride costs the same as a regular bus ticket.

Keep in mind that the Little Mermaid, Copenhagen's landmark statue, won't be on her perch during most of 2010 because the bronze goes on display at the World Expo in Shanghai, China. She is expected to be boxed and shipped away in late March to early April and will be back by late 2010.

Other conventional sights include the Tivoli gardens, Copenhagen's hippie enclave Christiania, and the Amalienborg Palace where Denmark's royal family live. All are free but Tivoli. The entrance ticket to the downtown amusement park is at $16.40 (85 kroner) and rides cost at least $3.80 (20 kroner).

Tivoli is open from late April to mid-September, one week in October and has a Christmas market in December. A free-access Christmas market can be found in Nyhavn across town. Yule treats, decorations and knitwear are sold from colored booths in the winter darkness.

Rosenborg Castle is a much-photographed landmark and home to the Crown Jewels. The Dutch Renaissance castle is centrally located in the Kongens Have park, where Danes love to picnic.

Leave downtown and head out to the Vesterbro district, right behind the central railway station. Once known for its working-class slum, red-light districts and dozens of sex shops, Vesterbro has undergone a massive transformation and is now a hip neighborhood with funky shops, trendy cafés, lounge bars, restaurants and night clubs.

North of Vesterbro lies the multiethnic district of Noerrebro, another working-class slum neighborhood-turned-hip. Its main street, Noerrebrogade, has been closed to cars to favor bicyclists, and the street is home to dozens of cheap ethnic restaurants.

Take advantage of free admission to state-run museums including the National Museum, the Museum of Danish Resistance and the National Gallery.

For cheap eats try a real Danish staple: red sausages, sold from small huts on wheels parked on major squares. The street vendors offer frankfurters, hot dogs and pork hamburgers. Food in Vesterbro and Noerrebro generally is cheaper than in downtown.

There are several youth hostels in the heart of Copenhagen where a room for two with toilet and bath cost from $100 (520 kroner) or half the price of a regular hotel room.

VisitCopenhagen.com offers tips for budget travelers:

http://tinyurl.com/ltwc4l.