How did Harry and his friends know so many places to disapparate to?

Question

In Deathly Hallows they traveled every day to a different place, for months, all over England. How could they know so many places? Or does apparition work even when you don't know the place you are going? And it's not that they traveled some miles near the previous place:

The weather grew colder and colder. They did not dare remain in any one area too long, so rather than staying in the south of England, where a hard ground frost was the worst of their worries, they continued to meander up and down the country, braving a mountainside, where sleet pounded the tent; a wide, flat marsh, where the tent was flooded with chill water; and a tiny island in the middle of a Scottish loch, where snow half buried the tent in the night.

Edit: I found a quote in the Half-Blood Prince, just before they went to the cave for the locket. that shows pretty clearly that you can apparate somewhere you haven't been before:

“Professor,” said Harry quietly, as the gates at the bottom of the drive came into view, “will we be Apparating?” “Yes,” said Dumbledore. “You can Apparate now, I believe?” “Yes,” said Harry, “but I haven’t got a license.” He felt it best to be honest; what if he spoiled everything by turning up a hundred miles from where he was supposed to go? “No matter,” said Dumbledore, “I can assist you again.”

Edit 2: And this contradicts the last one... So if they can apparate to a place they don't know why don't they apparate right outside Luna's house?

Where do the Lovegoods live, anyway? Do either of you know?” “Yeah, they’re not far from my place,” said Ron. “I dunno exactly where, but Mum and Dad always point toward the hills whenever they mention them. Shouldn’t be hard to find.”

Answer 1

They didn't know where they were Disapparating to in advance.

Bear in mind this quotation, as well as the one mentioned in the question.

Even without any new ideas, they continued to move through the countryside, pitching the tent in a different place each night for security. Every morning they made sure that they had removed all clues to their presence, then set off to find another lonely and secluded spot, traveling by Apparition to more woods, to the shadowy crevices of cliffs, to purple moors, gorse-covered mountainsides, and once a sheltered and pebbly cove.
_{(Deathly Hallows, Chapter 15, The Goblin's Revenge).}

It seems pretty plain to me that they were travelling to a random assortment of unfamiliar and obscure rural hideouts. They weren't hitting up places which they knew well from memory. Therefore, I think it's pretty unlikely that they'd have visited each individual location already. Rather, they were picking bits of the countryside at random - indeed, the fact that there was no pattern or logic in their choices was a key part of their approach. If there are nothing to link these locations (other than that they popped into Hermione's mind) then it makes it that much less likely that the trio would be tracked.

Of course, some of the locations were familiar beforehand. Hermione takes them to Tottenham Court Road and the forest which hosted the Quidditch World Cup. One of the sites she chooses is a place she's previously been on holiday.

“Where are we?” he asked, peering around at a fresh mass of trees as Hermione opened the beaded bag and began tugging out tent poles.
“The Forest of Dean,” she said. “I came camping here once with my mum and dad.”
_{(Deathly Hallows, Chapter 19, The Silver Doe).}

However, I think that these cases were the exceptions rather than the rules. There are simply too many locations for them all to be familiar.

On the wider point about whether Apparating somewhere unfamiliar is possible, I think that a parallel can be drawn with creating Portkeys. You don't need to have visited a location to make a Portkey to that location since Barty Crouch Junior made a Portkey that went to Little Hangleton without ever having been there before.

There certainly doesn't seem to be any contradiction with this notion in the theoretical description of Apparition. All that's stressed is that you need to pick a destination (any destination) and focus on it extremely hard.

“Step one: Fix your mind firmly upon the desired destination,” said Twycross. “In this case, the interior of your hoop...Step two,” said Twycross, “focus your determination to occupy the visualized space! Let your yearning to enter it flood from your mind to every particle of your body!”
_{(Half-Blood Prince, Chapter 18, Birthday Surprises).}

As is pointed out in the comments by The Walrus469 and Apostolis Kennedy, there are plenty of examples of people Apparating somewhere they've never been to before. Hermione and Harry Apparate to Godric's Hollow and up to 100,000 wizards Apparate to the Quidditch World Cup. Bellatrix and Narcissa also Apparate to Spinner's End, despite making it clear that they'd never been there before. Given that Apparating somewhere unfamiliar seems to be a pretty standard phenomenon I'd suggest that that's what Harry, Ron and Hermione were doing in Deathly Hallows.

Answer 2

You don't have to have been somewhere in order to Apparate there.

To the best of my knowledge, there is nothing in canon that indicates that you must have previously visited your intended destination in order to Apparate there, and a number of incidents that suggest you do not: for example, in Chamber of Secrets, Dobby used Apparation to travel to Harry Potter's house, despite never having been there before, and in Goblet of Fire a number of people used Apparition to travel to the Quidditch World Cup, held at a stadium that was built expressly for the event, on a site that was rented from Muggles.

I suspect the confusion arose from this quote from Half-Blood Prince:

'The important things to remember when Apparating are the three Ds!' said Twycross. 'Destination, Determination, Deliberation!'

'Step One: fix your mind firmly upon the desired destination,' said Twycross. 'In this case, the interior of your hoop.'

The easiest way to fix your mind firmly upon a destination is to be able to see it, and that suggests in turn that it is easier to Apparate to somewhere you have visited than to somewhere you have not. However, this does not mean that you can't Apparate to somewhere you have never been; at most, it suggests that it may be slightly more difficult to do so.

That means that, with a bit of practice, you can probably Apparate to a named destination, e.g., "Godric's Hollow", or to a destination shown on a map. It may even be possible to Apparate to a destination by description, e.g., "the closest forest north of here" although that is more speculative.

Answer 3

Hermione explicitly stated that she had been planning for this quest to find and destroy the Horcruxes. It is entirely possible that her plans entailed plotting several apparation/disapparation locations.

Answer 4

You know, if you have seen movie - Jumper, Apparition might work same. Person who doing it, feel same. You have to know the exact place you are apparating to, imagine it visibly. Problem is it imagine with details. As Sherlock said, human mind remembers only 62% what they see.