I've just come back from my first trip to Copenhagen and loved it. We really didn't know an awful lot about the place not having had any time to do much research beforehand. Amongst the few very handy tips I did receive was a link to a site called "Spotted By Locals" with the tag line "experience cities like a local."
Pretty self explanatory in the service it provides - city guides (both on web and iPhone app) focusing on good value rather than luxury of the best spots according to locals that reside there. The app for Copenhagen, which included a scrollable map displaying all hints & tips by category completely accessible offline, proved completely invaluable and went a long way to making our trip as enjoyable as it was.
If you find yourself abroad in a European city its likely there's an app from Spotted By ready to offer up a solid list of great places to eat, drink, shop and see. A total bargain in my opinion.
SPOTTED BY LOCALS