Just 25 min by train from downtown Copenhagen lies an old and beautiful forest and country area inhabited by wild (but friendly) deer. It's a vast, mysterious space for getting lost in and perfect for spacing out on mushrooms if you bring friends. Stay away on Sundays as it fills up with screaming children and zombie parents. Grab an ice cream on your way back at Bakken, the old David Lynch-ish fairground located at the outskirts of the forest.
Copenhagens bikelanes is all around the city. Its one of the best cities in the world to get around on bikes, there is even free bike servicestations around town:)