Well, I assume we are talking about places that are inhabited.
The actual mileage you get from darkness and cloudiness, as the one of your car, varies.
Darkest place on Earth
Definitely, the darkest city I know is Rujkan in Norway.
The site is close to the Artic Circle and the city is surrounded by mountains.
It is such a dark place that they installed a heliostat (a mirror that follows the sun) on the surrounding hills to get some sunshine.
Rujkan heliostat (notice the optimistic solar panels…)
With this installation, after a century of darkness, here you have the illuminated main square, where people can chat with their neighbors while getting a bit of sun:
Bring the bikini, let’s sunbath!
Notice that the sun is on the hills but the mountain does not allow it to shine on the town.
It reminds me of Berk, the city of "How to Train your Dragon":
Hiccup: This is Berk. It's twelve days north of Hopeless and a few degrees south of Freezing to Death. It's located solidly on the Meridian of Misery.
Cloudiest place on Earth
However, if you ask for the cloudiest place on Earth you have to travel to the Faroe Islands where its capital, Tórshavn, receives a meager 37 days per year of sunshine.
Depressing statistics for mean sunshine hours of this place when you think that you get SIX HOURS of sun in December.
January is twice as sunny, with 14 hours. Yay!
The true answer we all expect and suspect
Well, we all know that if you want to know the answer to this question you are… a vampire, of course!
If you are not one but you plan to become one, this article is for you.
With that in mind, I recommend Barrow, Alaska, ideal place for vampires .
First: There is no garlic or, at least, no garlic fields
Besides, you know, Americans and garlic… well, America is no Italy, although it may come as a surprise to you (pro-tip for vampires ) that Gilroy, California is the World Capital of Garlic, definitely not your hometown.
Secondly: Crosses are kept at a minimum as Inuits live there
I am assuming these guys prefer traditional native religion and they use walrus tooths and things like that in religious practices, always nice objects for a vampire to admire.
Thirdly: They are so Inuit-ized that they changed the name of the city to Utqiaġvik
This is additional security: imagine someone telling to Van Helsing: “I’ve found Nosferatu! He lives in Utqiaġvik”.
Van Helsing only possible answer is “Where?”.
Fourthly: The place is so dark that it has been the subject of a movie about it being the perfect place for vampires
The place is the site of the movie “30 days of night”, where a group of vampires take advantage of its extended hours of darkness.
Fifthly: Barrow (or Utqiaġvik for the locals) is so close to the Arctic Circle that it goes for two months without one single hour of sun
Of course, you have the problem of two months in summer where the sun never sets.
For that, you can rely on Rujkan and its tiny heliostat-illuminated square: spread your wings and fly away, via the North Pole during the last week of winter and stay away from the sunbathing place.
This place is so freaking cold that roads are unpaved: permafrost suffice
Sure, you can live in a northerner place, like LongYearByen (I swear I am not making this up).
It has a decent population (around 2.000 throats available) while places more to the north have all less than 100 souls (pun intended)
However, you must take in account the avalanches that destroy the town once in a while.
Longyearbyen before the 2015 avalanche that destroyed most houses, an alternative to Barrows
Nonetheless, Barrows has a large advantage: you are close to Sarah Palin and, who knows, perhaps Trump will visit one day (maybe he is already thinking of a wall between Alaska and Russia to stop missiles?).
Do us a favor, dear vampire reader: feed yourself that day.