Bornholm is an island to be outdoors on. A small island in the Baltic a nights ferry crossing from Koge just below Copenhagen or a short ferry-ride from Ystad in Sweden.
Cycling is very popular and it could not be easier to cycle round the island or along any one of the many cycle tours all over the island with very frequent clear signs and many places to hire bikes, park them or repair them. But if you are expecting flat Danish landscape think again. While the southern coast is pretty flat, inland and to the north boasts some of the highest hills in Denmark which is actually not too big a boast! In many places you can cycle off the road itself albeit you may be cycling alongside it. Even at the height of summer the traffic is not that great. Also all the buses helpfully have a bike rack on the back in case you get too tired although rarely was anyone seen taking advantage!
There are many beautiful beaches of which Dueodde is perhaps the most spectacular and yes you can swim in the Baltic it is not too cold but jellyfish can be a problem in many places. The castle at Hammerhus is spectacular and a boat trip out to the tiny islands of Christianso and Frederikso is well worth it.
Restaurants are perfectly pleasant and if you are into smoked fish there is a smokery in practically every village. A warning about eating out. Don't leave it too late. The Danes are all tucked up in their homes by just after 9.00 pm, so eating out late is not worth trying in most places. Many of the villages are very picturesque. Gudhjem has all the charm of some of the nicest Cornish villages in the UK and even the capital Ronne is no bigger than a small country town.
There is a surprising amount of interesting history on Bornholm - as well as Hammerhus castle there are many spectacular round churches, which might have a vague connection to the Knights Templars, and Bronze Age stone monuments just on the roadside. Germans seem to love Bornholm and so the quality of many tourist facilities is first rate. It will rain at some point so be prepared, but it is a very pretty spot and well worth a few days visit.