I can only second was has already been suggested.
Do a harbour boat tour as Edgar suggests, the cheap provider is called Nettobådene (Netto boats).
Edgar to be fair, Christian the 4th was a terrible Warrior King, he lost half the country to the Swedes. However is responisble for most of the old buildings in Copenhagen, including Rosenborg, the Round Tower and the Stock Exchange, so he's got that going for him.
Steves suggestion of Copenhagen Street Food is spot on, it's a great place. It's located in an old paper storage facility, called paper island (papirøen). Torvehallerne is more upscale, but equally nice.
Since you are staying in Christiania, try one of their guided tours of the Freetown. http://www.rundvisergruppen.dk/indexENG.htm
If you have something more specific in mind, other than, 'lesser know' sights, feel free to ask.