Copenhagen is a beautiful city and a notoriously good-looking population, but unless you are coming from Sweden, it’s also very expensive. Hotels are of pricey even during the off season, and are worse during the peak summer months. There are a few hostels, including four run by the government’s Danhostel program, and they can give your budget a break as long as you don’t expect much fun at the same time.
Most of the attractions are also shockingly expensive, so it’s good that strolling around the beautiful neighborhoods and the long Stroget shopping street are free. There are other free things to do, thankfully.
Food and drinks are also quite expensive, with a cheap meal in a restaurant nearly impossible to find. Self-catering by going to a supermarket can help keep costs down if that’s important. Beer in Copenhagen is quite expensive as well, and wine and spirits are even worse. Again, self-catering for the early part of the evening can really help.