When you arrive in Copenhagen, get settled in your hotel, turn in for a good night's sleep, and get yourself ready for some serious walking. Copenhagen maps out perfectly for the pedestrian, with nearly all the main attractions less than a half-hour's walk from Christiansborg Slot, at the center of downtown. If you're in town for an extended visit or would rather save your legs, the subway, bus, and suburban S-train networks can take you wherever you want to go.
Begin your first day at Rådhus Pladsen (City Hall Square) and follow Strøget, a pedestrian-only avenue, toward Nyhavn. Leave Strøget briefly at Amagertorv to visit the parliament building, Christiansborg; then, return to Strøget and make your way to the waterfront, all the while training an occasional glance at the shop windows in case anything catches your eye. Nyhavn is a good place to rest and refuel. You could take this opportunity to sample a classic Danish lunch of smørrebrød washed down with beer and snaps (schnapps). After lunch, head up to the royal palace of Amalienborg and take some time to explore the Bredgade area and find your way back to your hotel. If the weather is nice, the evening can be spent in Tivoli, but have your dinner outside the park to avoid the exorbitant prices. Early on the second day, take a boat excursion to see the city and its famed Den Lille Havfrue (The Little Mermaid) statue from the harbor. If you would prefer to get off and take pictures at the statue, make sure to take a DFDS Seaways sightseeing boat. In the afternoon, cross the inner harbor to the neighborhood of Christianshavn for a stroll along its canals toward Vor Frelsers Kirken (Church of Our Savior), where you can have a great aerial view of Copenhagen from the unique spire. This route leads you past the alternative compound of Christiania -- settled by hippies in the 1970s -- and beyond to the exclusive neighborhood of Holmen. The third day of your stay ought to be spent exploring the outlying Vesterbro neighborhood, with its cafés and shops. For art-lovers, the Ny Carlsberg Glyptotek would make a good several-hour detour on the way down Vesterbrogade.
Spend the first three days of your week as outlined above. The fourth and fifth days of your itinerary should be used to visit a few more of Copenhagen's fine museums. Among the best remaining are Rosenborg Slot and the Dansk Design Center, neither of which should be missed. A morning visit to Rosenborg Slot can be followed by an afternoon tour of the botanical gardens and a dinner in Nørrebro. Alternatively, you could head north from the castle and while away the afternoon along the paths and moats of Churchill Park, grabbing your evening meal in Østerbro. The final two days should be spent on day trips outside of the city proper. A day in Charlottenlund should begin with the astounding French impressionism collection at the Ordrupgaard, which can be followed with a snack at the adjacent café and a few hours at the town's pleasant beach, which is considerably less crowded during the week. Use the final day to skip town again for the verdant Deer Park in Klampenborg, or the seaside town of Dragør.