No, no, Kubrick hated shooting on location. All those Vietnam scenes in Full Metal Jacket..? Filmed right next to London.
Now, he did fake the moon landing, of course, that's why NASA gave him the lens he used to make every single frame in Barry Lyndon look like a period painting... but much like with the start of 2001 (also filmed in London), he wanted lots of location pictures for reference (he didn't want to go there, wherever it was, but he had no qualms whatsoever about sending other people), so he demanded NASA send astronauts to the moon anyway to take those pictures, and the official moon landing was faked using those pictures taken in the real one as reference.
And do you know how he managed to make every frame in that film look like a period painting..? A very particular and expensive lens NASA gave him.
(Of course, though, while the man despised filming on location, he required massive amounts of reference pictures to build his sets, so even though the official moon landing was fake, NASA still had to get some astronauts there first to take those pictures for him.)