Møns Klint claims its OUV from the glacial landscape formation and being part of one of the world's largest glaciotectonic complexes. But much more significant what is described as “scenic value”, which means the cliff is simply nice to look at.

As the aesthetics are a big part of this, I selected a day for the visit I knew the sun would shine. We took a rental car from Copenhagen Airport and drove there, with a detour to Roskilde and a stop at the unimpressive Borgring. Once you are off the freeway, the drive is very scenic, with typical Danish landscape, great old houses and lots of green. You can drive to the GeoCenter Møns Klint, where there is parking (6 EUR for 1 day), walking paths and stairs to the beach.
Getting there by public transport is possible I guess, but you would need to take a train to Vordingborg, a bus and still find a solution for the last 6km. So, I would not recommend it.

At the GeoCenter we opted for hike number 4, further up north along the cliff through the forest, down the stairs and back along the beach. The hike was fantastic, with great views at the cliff. I assume the views might be more restricted once all the trees have their leaves back. 
Unfortunately, the info board at the GeoCenter did not mention, that the stairs we were supposed to use as a turning point, were closed (and it seems not since yesterday). We hiked on to the next stairs, which doubled the distance of the hike instantly to a total of 3 hours and caused some discontent by my son. It was nevertheless a great hike. More walking equals more cliff views.
The walk back along the beach also head its obstacles. Several trees fell down the cliff, blocking the beach and forcing us to climb over them. All in all an exciting route, that requires a certain fitness level.

Be aware that the whole island has not a lot of infrastructure. There are a few restaurants in Stege, but they were either closed or we did not like the options. We ended up driving to Præstø for dinner.

The cliffs make a great daytrip from Copenhagen and would certainly not be the worst WHS in Denmark.