I have absolutely enjoyed my 2 nights stay in Maria's apartment on Krystalgade 9A (right next to Round Tower, 5 mins to Strøget, max. 45 mins to airport) and will definitely recommend it. The interior design of the living room / study is genious and I really liked the overall rustic feel of the apartment. The kitchen was fully equipped for cooking, which is very handy considering how eating out can be expensive in CPH. The bathroom was very small as expected from the reviews but I didn't mind it so much; the other good points of this apartment totally outweighs the small bathroom. I understand from Maria that her plan to enlarge the bathroom requires government approval as the building is historical (which makes it extra special, learning how locals try to work around heritage of the city!). The location is prime. Although check in was later in the day at 5pm, it's easy to store luggage at the central station (50DKK for small lockers, 60DKK for large) as you do initial exploration of the city.
Final point - as a solo traveller, Sofus the black cat makes very good company given that "meow" is the same in every language. : )