Admire all the hot Danes. By far, Denmark had the highest percentage of attractive people in the countries I visited on my recent trip (including Germany, Czech Republic and Austria). It was also by far the most expensive country on that trip, so good luck not spending a fortune.
As for stuff to do, there's the obvious tourist stuff in Copenhagen (the SEVERELY overrated Little Mermaid, the Opera House, Nyhavn, Stroget, Round Tower (great view from up there, BTW), Tivoli, etc.). If you want to get away from the city, there's the Viking Ship Museum in Roskilde and Kronborg Castle in Helsingor, both short train rides away in different directions from Copenhagen; personally I liked getting a more up close and personal view of smaller Danish towns.
From Helsingor, it's a 20-25 minute ferry ride to Helsingborg, Sweden in case you felt like adding another country to the list of places you visited. We wound up going over there just because the ferry ride was short and cheap--it's worth devoting short trip to if you have time.