Nicolai's place was very nice. It was very close to all sorts of Meat Packing District dining options and bars. It was also very, very close to a train station which was a quick 1 stop from Copenhagen Central (and Tivoli), and 2-3 from downtown proper. You can be walking around in any of these areas within 10-20 minutes from leaving Nicolai's flat. That's not to mention the local neighborhood bar there on his street, Cafe 33. Great place to meet friendly locals. Kihoskh, which is a really neat little... cafe? Corner store? Upscale 7-11?... is right down the street and has coffee, milk, soap, a fantastic beer cellar, and board games for purchase. Mad & Kaffe should be a destination for breakfast/brunch. If you are a meat-eater or beer-drinker, DO make your way to Warpigs for dinner.
Relevant details for parents travelling with small children:
There are stairs between the street and the one-floor-up apartment. Your stroller is easily and securely stored on the ground floor (still about 3 steps up). There is a bunk bed available for kids. The lower bed has a safety railing but would not be good for infants still sleeping in cribs. Bring your pack 'n play. There is also no bathtub for bathing children not accustomed to showering so bring a wash cloth for a sponge bath. There are a plethora of toys which will keep all ages of children busy, including a child-sized kitchenette and table with chairs, duplo-legos, and tricycle. There is a high-chair available and lots of space for babies to safely crawl around. There is also a neat inner courtyard with playground items, including a sandbox and communal toys. The back stairs used to get there are rather steep so be careful. There is an inexpensive laundromat down the street you can use but the controls and dials to get them to work are not immediately obvious, if you are not used to the system. I saw a laundry room in the building where the apartment is, but not until I had already used the neighborhood laundromat.