Andreas & Tania's place was the perfect choice for getting to know Copenhagen. The place is very easily accessible from the airport and the city, within walking distance from the metro and many bus routes. It is right at the 'it' area where locals hang out, with many good choices for drinking and dining just there. The apartment itself is clean and very stylish, and very nicely decorated, and as a bonus it has just recently been renovated so it has a modern feel as well. Be prepared to climb 5 levels of stairs to reach the apartment though.
Nonetheless, it is 100% recommended, they have been excellent hosts, the apartment is great and strategically located, and we honestly enjoyed our conversations with them.