In winter, a visit inside the beautiful glasshouse Palmehuset (the palm house) will get you properly warmed up. The spiral staircase will lead you 20 metres up to the top of the glass dome.
If you feel inspired to do a little gardening yourself, stop by the flower shop where they sell a selection of the 13,000(!) plant species that the garden houses. In the summer season, the outdoor cafe is also open (when the weather allows).
2B Øster Farimagsgade, 1353 København K. Entrance to the garden from Øster Farimagsgade and Gothersgade (the corner of Øster Voldgade).
Tel.: 3532 2222
Open: Summer (May-Sep) 8:30-18, winter (Oct-Apr) Tue-Sun 8:30-16. Palmehuset is open 10-15 every day, though closed on Mondays in the winter season.