Djurgården is a lush and green island full of museums and parks. Junibackens Museum (http://www.junibacken.se) and Aquaria Water Museum (http://www.aquaria.se) offer something for the younger generation as well as for their parents. Thilsta Gallery (http://www.thielska-galleriet.se) offers an unique collection of Nordic art as does Prins Eugens Waldemarsudde (http://www.waldemarsudde.com)
The old hunting island of the Royalty is a good place to bicycle around with your own pace. I would spend some time relaxing under the apple trees at the Rosedals garden. There is also café and a shop that sells ecologically grown vegetables and plants to take home at the garden.
Since it´s no longer legal to build on the island along the way you will see some beautiful architectural gems. Swedens high class rubs elbows here on the shores. The famous families such as Wallenbergs and Bonniers own luxurious mansions in Djurgården. There are also some wonderfully restored wooden houses scattered around the island.
There is even a swamp area where you can spot birds. If you are traveling during a week day there is a good chance that this area is full of small kids trying to find out more about the natural beauty the surrounds them.
There are few restaurant suggestions along the biking trail. Lisa på Udden (www.lisapaudden.se) offers nice Marina views at Biskopsuddes Marina. You could even have delicious and inexpensive lunch at Kaknästorget (http://kaknastornet.gastrogate.com) The Lunch is served high up in the television tower. The price for this exotic lunch is 95Kr or 8,5€.
See the whole route on my maps.There are some exotic accommodation suggestions along the way.
CLICK HERE
http://maps.google.fi/maps/ms?client=firefox-a&hl=fi&ie=UTF8&msa=0&msid=115002011674228075671.000469dc71f4abe9b620f&t=h&z=13
Rent a Bike at:(Check the My google maps above for directions)
Djurgårdsbron sjöcafe or
Gamla stan Cykel