You have already seen the major sites of the capital city, Copenhagen, but you want more! Here is a short list of what to do next on your Danish tour:
1. Freetown Christiana- Christiana is an alternative, anarchist society started in 1971 when people broke down fences and started squatting in old military barracks. These Copenhageners have lived by their own rules since, but not without some angst. The drugs sold on Pusher Street, AKA "The Green Light District", have caused some turmoil and for years there were police raids and some arrests. The sights and smells of Pusher St. may be the definitive Christiana, but wandering beyond this row of dealers there is much more to see. The communal living neighborhood is full of beer gardens, restaurants, shops and gardens. The one thing, not to miss, is the self-made homes and very unique architecture. One important rule here is DO NOT photograph anyone on Pusher St. but the architecture is very instagrammable :) Culture Trip shares a great blog that outlines what to know before you go!
2. Kayak Republic - Seeing Copenhagen from the water is a great way to experience this city and chillin' in a kayak is an interesting alternative to your typical boat tour. Kayak Republic offers 2 hour tours, everyday at 10:00 or private, scheduled tours that will wind you through the canals in the heart of the city. Your paddling parade starts at Knipplesbro (hehe) and then you wander past "new, old and hidden parts of Copenhagen, making stops to talk about the history and culture of the city." You will be sure to see some sites you missed on foot. No kayak experience necessary and there are single and double person kayaks available. After you have shared the beauty of the city, from a different angle, and parked your kayak, head to the Kayak Bar for some food and drinks. You can make arrangements with Kayak Bar, before you even set out on the waters, and then come back, relax and post your pics :)
3. Copenhagen Street Food - Here we have food trucks, there they have food halls and markets and shipping containers! In 2011, the market Torvehallerne opened up, right in the city center. The market consists of 2 beautiful glass buildings, one with savory offerings and the other with sweet. This is a great place to wander and take in the variety this market has to offer. If you decide to just grab a coffee and something sweet, Coffee Collective gets rave reviews and Granny's House looks like a great place to feed the sugar craving.
Another spot for street food that seems very hip and fun is Reffen, a market in an old shipyard with a wide variety of food being served from old shipping containers, a small beach to picnic at and plenty of live events for your entertainment. This market believes in sustainability and rewards it, they represent more than 18 different nationalities in the food offered and they offer workshops and events, all in a one of a kind setting that has brought life back to the old shipyard!! It takes about 10 minutes to get to Reffen from the city on bike, bus or boat. Then bite into some Indian, Mexican, Nepalese, Filipino, Greek or classic Danish dishes-like S'Morebread or a fried pork sandwich. This place is a perfect spot to end your visit and hit up on your way to port :)
4. More eclectic stops: Are you a Twin Peaks fan? If so, you might want to grab a coffee at the Log Lady Cafe- themed after the TV show. If you like board games, old flicks and interesting entertainment, all served up with hygge, then you should totally check out Huset KBH. And not far from the original Little Mermaid statue you can spy an alternative mermaid. There are a few very interesting sculptures in Bjorn Norgaard's Genetically Modified Paradise, at Dahlerup's Square, on the water (may want to include on your kayak tour).
For great information on these spots and much more about Copenhagen, check out the blog Hand Luggage Only, where you will find a lot of insider tips. I don't know how much you can pack in over a weekend, but just remember you can rest later, and this may be your one time to experience this cosmopolitan city with so much to offer.