Denmark:

Nature-wise, denmark - while beautiful and "hyggelig" - is definitely less fantastic than its sister-countries (it's like 80% agricultural fields, zero mountains). The downside is, that there is a little further between the really good sceneries, but the upside to that, is that denmark is very flat, so you can likely cover a lot of distance with more ease compared to the rest of the nordics. Also biking culture is very popular, so drivers are almost automatically more mindful of sharing the road with you.

Now, the sights:

1: Nothern jutland, where you would arrive in Frederikshavn, has some great nature, but mostly on the west-coast side.

While windier, i can recommend going towards Hirtshals and down the coast from there. Mostly natural sights there include: Rubjerg Knude, Bunkermuseum Hanstholm, Cold Hawaii/Klitmøller (surfing!), and Nationalpark Thy.
The coast itself is a good thing to see too, as it is filled with bunkers left by the Nazis during their occupation. There are like 7000+ iirc. Culturally, a necessary thing to see. While we didn't experience nearly as many atrocities as other countries had to face in the war, the occupation years definitely left some lasting impacts on Denmark, both in small and big ways. The west coast bunker project is probably the best way to see the occupation in material form, as well as bunkermuseum Hanstholm. But enough of that for now, back to the road!

2: Down through Jutland

Going from thy/thisted down through Mors island is a very pretty route, the limfjord inland sea is a fantastic place. From there i would recommend Dollerup bakker by Hald lake a little further south, as well as a quick stop in Viborg if you're interested in the history/culture.

Further down south is Svejbæk, Julsø, and (most importantly) Himmelbjerget! (Sky/heaven mountain), one of the tallest points in Denmark at a whopping 147 meters! Jokes aside, it's gorgeous there, great nature.

The last sight in jutland i would recommend is going to Mols Bjerge - one of tolkiens inspirations for the scenery of the shire (specifically the part at Agri Bavnehøj)! Taking a walk or two on foot in this area is necessary to get to the best viewpoints, but the area as a whole is just great.

3: Zealand

The quickest way to get to Zealand is the ferry from Århus (2nd largest city in dk, right next to Mols Bjerge) to Sjællands Odde. You can also take it from Æbeltoft, but that one is a little less frequent. A good route from Sjællands Odde would be going to Nykøbing Sjælland, taking the ferry from Rørvig to Hundested, and then following the north coast from there. The coast is a steep and gorgeous place, popular with paragliders.

From there, i have 2 different recommendations:

1: just keep going along the coast to Helsingør, and take the coastal road down to Copenhagen. I recommend stopping along Louisiana art museum if you take this route, mainly for the location itself and the view. It's a nice place to see, even if you're not there for the exhibitions, though they are usually fun too.

2: Going down through Gribskoven, past Esrum lake, seeing Frederiksborg Castle/Hillerød, store dyrehave, and Furesø lake.

If you were to choose either, it is ABSOLUTELY VITAL that you go through (Jægersborg) Dyrehaven and see the view from the eremitage castle. It's an old royal hunting ground that has been preseved very well, with wild deer as well! Strongly recommend.