Greet the day by taking in the view from the deck of your hotel, CPH Living, the only floating hotel in Copenhagen. The converted freighter has twelve rooms, and makes the most of its unique location off the coast of Christianshavn Island with floor-to-ceiling windows. You can breakfast here in the dining room or step off the boat and walk to any of the small coffee shops that dot the harbor.
One of the best ways to learn the layout of the city is to see it from its waterways, so continue the aquatic theme by renting a boat or boarding one of the many guided cruises available. The best route is to head up the main harbor past the Opera House, Kastellet, and The Little Mermaid, before turning to sail back down the Frederiksberg Kanal past Slotsholmen, the Bryghus, and Holmens Kirke, ending back at Nyhavn Harbor.
From Nyhavn Harbor it's a short metro ride on the M2 line to Amager Strand Station. A ten-minute walk will take you to Amager Park, a luxurious beach on a man-made island with 4.6 kilometers of soft white sand. Summertime brings crowds here to sunbathe and wade in the cold water, but there's plenty of room for everyone, with areas set aside for sport and picnicking. The views here are sublime, including the enormous bridge that connects Denmark and Sweden.
Pack up your towels and board the metro back towards downtown, to pick up a picnic lunch from Slagteren ved Kultorvet, a neighborhood butcher shop that sells some of the best sandwiches in the city. Walk a short few blocks north to Kongens Have, a public park that dates back to the 1600s, where you can spread out under the trees and watch passers by as you eat.
After lunch walk five minutes to the Rundetarn, or Round Tower, the oldest astronomical observatory of its kind in Europe. You can burn off some calories by walking the cobblestone ramp all the way to the top, where the views of the city and its surroundings make for amazing pictures. There's also a small museum where fans of astronomy can learn how that science developed in medieval Scandinavia.
When you emerge from the Round Tower, take some time to explore the surrounding neighborhood, which is called the Latin Quarter, or Pisserenden. The University of Copenhagen has its campus here, making it a lively, youth-oriented corner of the city with excellent shopping and cafes. You can join a guided tour, or just strike out in any direction and enjoy the beauty of the cobblestone streets and public squares.
For dinner stop in at any of the restaurants here in the Latin Quarter, most of which serve an affordable menu scaled to student budgets. Health food nuts will enjoy 42 Raw, where the entire menu is vegan and organic - the gluten-free pizza is surprisingly good - or stop in at Cafe Halvvejen, a friendly pub serving Danish home-style food like brown bread with herring and grilled sausages.
After you've eaten, hop on the 6A bus from Norreport Station to Vesterbro, to have a few drinks at one of the local pubs. Try Vela - the only bar in Copenhagen that caters exclusively to lesbians - where the atmosphere is laid-back and sporty, with lively music, foosball, and pool tables. Or stop in at 1656 - a low-key bohemian drinking hole with a menu of fun, fresh cocktails, and a cheeky design scheme - before heading back to the hotel for some well-deserved rest.