"I know the city."
Translation:Jeg kjenner byen.
In context can you go further into why jeg kan norsk works, because it doesn't really make sense in english.
At a guess, it's similar to "Jeg skal til byen", "I shall (go) to the city". After modal verbs, you can often leave out the.... the other verb (don't know what it's technical name is).
That said, my Haugen's dictionary does list Deliciae's usage as the third meaning of "kunne": "know (eg a language, lesson, poem song, etc); know how to (eg perform a skill, play a game, etc): kan du norsk? do you know Norwegian; kan du spille sjakk? do you (know how to) play chess?"