Recommendations for what to see/ where to eat in Copenhagen

[Surok]

Going to be in Copenhagen this weekend for a meeting, but will have Saturday evening and Sunday free. I'll be staying...eh....somewhere near the train station.

Any recommendations for what to see and where to go?

Also looking for restaurant/ cafe recommendations, particularly local food (I'm not that interested in 'Modern European' which you can get pretty much anywhere) and nothing too expensive.

Incidentally, I adore herring with a passion that borders on the obscene - so bring on your herring recommendations!

[Blue Mood]

The only sightseeing place I know is the Little Mermaid statue. I think herring should be easy to find though.

[Left Hand of Dorkness]

The Lejre Experimental Centre is freakin' awesome. I'd say it's well worth a day.