Start in Copenhagen, spend 5 nights in excellent hotels and 4 days cycling an average of 30 miles per day. Your luggage is waiting for you each evening when you arrive at your new hotel.
All major sights are within walking distance of the hotel.
How about a stroll down Stroget, the long pedestrian street. Not forgetting the side streets of course. Here you will find the old medieval part of Copenhagen as well as many excellent restaurants. You will be riding near the coast all day. Louisiana, the museum in Humlebaek, enjoying world acclaim for its exhibitions of modern art as well as for its picturesque location, is definitely worth a stop.