When you get there buy a Copenhagen Card that gives you free entry to museums and unlimited use of the bus, train and metro. Copenhagen’s new metro is excellent and was put in in about 1/3 the time it took us to put in the Luas and at less than 1/3 the cost. For things to do just buy the Lonely Planet guide on Copenhagen which is as good as any you’ll get and follow their recommendations. Friday night is the big night out in Copenhagen when everyone goes out to get p*ssed. Then they revert to their conservatives selves for the rest of the week. There is a good selection of restaurants, bars etc. in the Nyhaven area, and also less touristy ones in the streets parallel to the Stroget (walking street) but check out the prices before you enter. Copenhagen can be expensive for food and drink, but wine in off-licences is about Dublin prices. For souvenirs, crystal, design goods, etc. go to Illums department store on the Stroget. You should also visit some of the surrounding towns near Copenhagen like Roskilde with the Viking long ships (the big one was built in Dublin), Helsingor with ‘Hamlet’s castle’ etc. and to see Danish life. There's more than enough to visit to keep you occupied for the weekend. You can also cross over to Malmo is Sweden, which is less expensive than Copenhagen, and more laid back. Check out: [broken link removed]
If the weather is ok, Christiansborg Castle is worth visiting.