Nadja, the landlord, was welcoming and helpful, and speaks perfect English (like most Danes).
We loved everything about the apartment. It's small, but is the right size for a couple, and perhaps a small child. There's a bedroom, a kitchen, a living room (with another bed), and a bathroom. The bedroom and kitchen look out over a charming, quiet courtyard. The kitchen is well-equipped except, oddly, for a microwave. Maybe there is one, though, and it's just so Danish we didn't recognize it.
Everything is sparklingly clean. Even the floors are white (so take off your shoes!).
The shower is small, and may take a little getting used to, for Americans, but I found it all eminently practical.
There are several great cafes, restaurants, and convenience stores within a block or two.
There are excellent bike-rental facilities nearby. We used, and recommend, Bisikeli. With a bike, all major Copenhagen attractions are within an easy ten-minute ride. It's easy to rent a bike for a week, and just park it in the apartment's bike parking area.
The apartment provides no off-street car parking, and on-street parking is rare and expensive. If possible, DO NOT rent a car in Copenhagen. Do what the great majority of Copenhagen residents do, and ride bikes. Physically-separated bike lanes make it safe and fun, and the city is almost completely flat.
Note that it's what Americans would call a third-floor walk-up. There's no elevator, so if there's a problem with stairs, this may not be a good fit.