I am so sorry to post this without digging deep into this Forum (which I love), but we have a spur of the moment chance to head to Copenhagen. Where is the charming hear of the city, where we could walk to sights and local restaurants. Where can I feel like a "temporary local"? Thank you for responding and, again, my apologies because I am sure buried in this treasure trove of traveler posts is the answer I need, I am having to do this on the fly...
I believe it's referred to as "Indre By". That's the oldest part of the city where you'll find the beautiful buildings and historic sights.
Anita is right. Indre by (inner city) is the old, medieval part of Copenhagen. Is is some times refered to as the Latin Quater in some guide books as well.
However being near the sights and living like a local does not often go hand in hand. The inner city is not really a residential district, it is more a commercial and shopping district. There are of course locals living there, but also quite a few offices, shopping streets and of course other tourists.
Another nice neighborhood is Christianshavn, which is an old canalled neighborhood inspired by Amsterdam. It's close to the sights, very atmospheric and has a lot fewer chain shops and offices than the inner city.
I'd have said Nyhaven, but Copenhagen is a very compact, walkable and beautiful city in the main. If you haven't booked accommodation, we stayed at the 'Wake Up Copenhagen' which is ten minutes from Nyhaven on foot. We got a reasonable three night deal for room only (lots of cafes and supermarkets nearby for breakfast). The rooms are 'compact' shall we say, but clean and secure and to be blunt we really only slept there - out and about all the time! We walked all round the city, covered miles and miles, and took two side trips both by rail to Helsingor (Elinsore) and secondly to Roskilde, the latter to the longship museum which was brilliant and shouldn't be missed if you get the chance to go.
Hope you have a great trip!