7 1/2 hours layover in CPN Airport

Cape Rodney in Papua New Guinea?

Do you mean Copenhagen, CPH?

Both the metro and the trains run into the city, it's just minutes away. You can do a great deal with 7-1/2 hours in Copenhagen.

Kind of the long way around to get to Denmark going through New Guinea? ;-)

Yes, CPH; thanks! Another trip we will schedule more time in Copenhagen!

Thanks! I’ll inquire at the tourist information desk.

You have plenty of time provided your arrival flight is on time. The city is very close to the airport and public transport is just minutes away from the center. Conservatively you should have at least 3-4 hours in town, maybe more. There is baggage storage at the airport if your bags are not checked through.

Yes, easy train ride from CPH to Central Station:
https://www.visitcopenhagen.com/copenhagen/taking-train-copenhagen-airport

If you want to go to Copenhagen Central Station, the train is your
best option.The train station is located by terminal 3. You can take a
free shuttle bus from terminal 1 to terminal 3, which will take 5
minutes.

The trains run every 10 minutes during the day and will get you to
Copenhagen Central Station in about 13 minutes. During the night the
trains run 1-3 times an hour.

Copenhagen is very walk-able Enjoyed the Netto Boat tour:
https://www.visitcopenhagen.com/copenhagen/netto-boats-gdk585017
I don't remember how long the tour lasted. The boat is about a half hour walk from the Central Train Station, longer if you stroll. Bus ride would be shorter.

It's easy to take the Metro into the city. It can drop you off at Kongens Nytorv, adjacent to Nyhavn and one end of the Stroget shopping district.
The train will take you to the main train station on the west side Kobenhavn H, next to Tivoli and the Meatpacking District restaurants.
There's also a bus and it's cheaper but also slower, and it's not worth it for your limited time.

The fare is the same, no matter if you travel by bus, train or metro.
You can Copenhagen get door-to-door directions with public transportation on www.journeyplanner.dk.

I believe the free shuttle bus mentioned above is the shuttle bus to Den Blå Planet (The Danish National Aquarium). It's relatively infrequent and doesn't operate year-round. If anyone is interested in visiting Den Blå Planet you can read more about the shuttle here: https://denblaaplanet.dk/en/visit-us/shuttle-to-den-blaa-planet/. Den Blå Planet is also quite close to Kastrup metro station (just one stop from Copenhagen Airport, fare: 24 DKK). So yes, it's a waste of money to take a taxi from the airport to the aquarium. It looks like you learned that the hard way - hopefully others can learn from your experience :-)

Hi Anne, I am not sure if I could be of any help but here goes.
Last time we were in Copenhagen we arrived by a cruise and left by plane. It was disembarkation day and we had to leave the ship early. Our flight was late afternoon and we didn't feel like spending that precious time sitting and doing nothing at the airport. So we arrange a private tour. They picked us up from the cruise port and at the end of the tours brought us to the airport. If I am not mistaken it was about 4-hour tour. We had a great time! ok granted, you will not be able to see all the sights. But at least we had a stroll and saw the little mermaid, walked through the Tivoli gardens and saw the Amalienborg Castle (where the royal family lives). And the guide told us many stories that we would not have known if we would have done it on our own. Not sure if this could be of any help, but maybe you can contact Anastasia Tours and ask what the possibilities are. We had great contact with them when we were booking all our baltic tours.
Good luck!