Here is top ten things to do by travelers....
3 are Art and one Garden..
1. Strøget Attractions
2. Glyptoteket Contemporary Art
3. Tivoli Attractions
4. Rundetårn Attractions
5. Statens Museum for Kunst Contemporary Art
6. Kongens Have/Rosenborg Slotshave Parks, Gardens
7. Nyhavn Attractions
8. Open Top Tour Guided Tours
9. Krasnapolsky Contemporary Art
10. Rådhuspladsen Attractions
Go to link and click on more things to do and browse by catagory
Here is top ten hotels 5 and 8 seem reasonable
1. Radisson SAS Royal Hotel $377
2. Marriott Copenhagen $158
3. Hotel Sankt Petri $339
4. Hotel D'Angleterre $314
5. Maritime Hotel $123
6. Hotel Imperial Copenhagen $199
7. Sofitel Plaza Copenhagen $306
8. Danmark Hotel $118
9. First Hotel Vesterbro $263
10. Radisson SAS Scandinavia Hotel $235
Here is top ten places to eat...
1. Kommandanten French
2. Vesuvio Italian
3. Italiano Italian
4. Restaurationen French
5. Nyhavn 17
6. Khun Juk Oriental Thai
7. Al Mercante Italian
8. Slotskælderen - hos Gitte Kik
9. Grønnegade French
10. House of Korea Asian
Read the user reviews from Yahoo and the Web they have great ideas and clues to enjoy your stay!