I've stayed at the Absalon- lovely bedrooms!! Very central
Having lived in Copenhagen my personal pics would be the scandic in Frederiksberg - lovely leafy area , good metro into centre , (8 minutes) nice bar lounge area and a big modern shopping centre next door, the Radisson is nice too in a slightly dated way but rooms have great views as it's a high rise hotel, 5 minutes walk to metro at islands Brygge, the Marriott on the waterfront very good, very modern architecture area and walkable into town , finally the lovely new NH in Christianshavn, very nice area, canals etc, on metro and some lovely bars and restaurants in the area, or a quick 15 minute walk through christianshavn to Nyhavn.
In Stockholm - you simply can't beat the Rival (owned by one of the Abba guys) we've stayed their 5 times, it's in a pretty square, 3 minutes to metro, 5 minutes on metro to centre of city - absolutely lovely vibe, staff and decor.
The Radisson in ostermalm is also very nice, posh upmarket shopping area but hotel faces waterfront