Denmark doesn't have deep gorges or high mountains but rolling green hills, forests, small villages, city centers 5-800 years old, a lot of fjords and small islands, many white sand beaches.
In september, you can go to any beach on a workday and have kilometers for your self.
you can get a map in the tourist info with "margueritte routes" which are special signposted roads taking a motorist through Denmark on small scenic roads passing different sites. I even use these for bicycling as they generally are very low traffic roads but, being Denmark, very well maintaned.
You might want to stick to the east or west, as the great belt bridge costs 44£ for a return ticket.
The westcoast of Jylland is rougher than the rest of the country, with western winds being the prevailing winds in DK but is magnificent in an autumn storm with the North Sea crashing on kilometer wide white beaches and the foam rolling in the wind, where you'll be able to "fly" standing on a high sanddune in the wind.
Some of the beaches are navigable on a motorcycle :-)
there are many castles with public access, many dating back 4-600years with moats around and great museums.
The Danish National Museum is fantastic, especially their inuit collection of more than 100.000 thousand pieces, mostly from Greenland. Unique in the world.
The Vikingshipsmuseum in Roskilde has four ships found in the water just outside the museum and dug up. They have the largest vikingship in the world. A copy of a year 1020 warship, found under the museum and built exactly as the original with the same materials and tools. It was originally built by danish vikings in ireland and sailed to Denmark, when half of the british isles were danish ;-) . You might even go sailing in a vikingship but no plundering please.
Vikingeskibsmuseet Roskilde: The Viking Ship Museum in Roskilde, Denmark
There is a lime cliff at Møns with fossils and at Fur in a kind of clay cliff, there are fossils from a sea, 50mill. years old
Fursund Turistforening - Fossil hunting
If you are interested in Cobra art, the Asger Jorn and the Carl Henning Pedersen museums in Jylland have the biggest collections of their art in the world.
You don't say where you will be in the country but this site may give you some inspiration.
The Marguerite Route - Denmark - VisitDenmark: The official guide to Denmark with Danish tourism and travel information such as hotels, map, flag, Copenhagen info etc.
If you need more concrete infos, just say so.
I can't take you around, as I'm still a lurker, shopping for a new bike. I only have two trackbikes in the garage.
From a trip from Denmark to Ireland:
Carl Henning Pedersen
Westcoast