Take a daytrip by train to the Swedish city of Malmo. Malmo is located just across the famous Oresund Bridge. A trip by train takes only 35 minutes and a return ticket was only 140 DKK in 2004 (less than 20 EURO). Malmo is Sweden's third largest city and is well worth a day trip.
Because Copenhagen is so close to the Swedish coastline , I decided to take the ferry across to Malmo . The ferry leaves Dragor in Copenhagen at frequent times for the short crossing to Nimhamn in Sweden. From the harbour you can then take a bus into Malmo itself. The bus journey will only take 20 minutes or so and the actual ferry crossing should only be two hours maximum. There you have it , two countries in two hours!
UPDATE......... since my trip in 1995 , there is now a road bridge spanning the sea between the two countries ( but my journey is much more fun!!)
One of the nicest places I know in the south of Sweden (and they are many), Ven is an island which used to belong to Denmark but when Sweden took the eastern parts of Denmark, they insisted on Ven so the Danes couldn't fortify it. Apart from being a gorgeous place, known for its "backafalls" which are steep cliffs down to the sea, Ven is also famous for being the home of the famous Danish 15th century astronomer Tycho Brahe. Today, there is nothing left of his palace but you can see a great exhibition about him in the 19th century church in the grounds and wander around what used to be his garden as well as visit a little astronomy show. The island is small enough for you to cycle around in half a day and that is indeed the way to get around here - cycle rental is big business, taking you around the many food establishments and art galleries. The main route here is by boat from Swedish Landskrona but in summer, and at some holiday, this makes a great day out by boat from Copenhagen too. Read more on my Ven page if you too want to eat, drink and bike.
Well a little contradiction on this one but if there is a moment when you want something different to do during your visit to Copenhagen I would advise a day trip to Sweden. We took the train from Copenhagen Central Station to Malmo CS. It takes only 3/4 of an hour to get there and the train goes 24/7 every twenty minutes or so. The rates are, compared to other EU nations, quite moderate and the trains are quite luxurious. Just plug in your headphone in the console above and listen to music or radio while enjoying the view from the 16 km Oresund bridge. Lovely.
Malmo is a nice place to visit. Inexpensive, people are friendly and a lot of interesting architecture. We where on Malmo CS trying to sort out how the ticket machine for credit cards worked and in a flash there was a very friendly lady appeared whom was willing to explain the Swedish machine for us. It was some kind of hostess employed by the railway company to help out to tourists. A service we've never encountered during railway travel in the past anywhere.
Across the sea from Copenhagen, in another country, lies one of the major cities in Europe. This was a city that once was visitable only by ferry, but since the great wonder of the Oresund bridge was built, it is now accessible by a train. It's so easy and close that many people live in Malmo and work in Copenhagen.
Malmo is Sweden's third biggest city, and famous for its diverse population, great architecture, and the successful football team Malmo FF, home to goal scoring legend Zlatan Ibrahimović. Probably its two greatest sights are both buildings, both at different ends of the age spectrum: the Malmöhus Castle and the Turning Torso. The latter is the tallest building in Scandinavia.
If you're in Copenhagen I guess there's a good chance you will visit Malmo while its only just a train ride across the Oresund Bridge.