I don't know how far above the Moon the command module's orbit was, but the Moon is about 3500 km in diameter, so when the command module was on the opposite side of the Moon from the lunar module, the astronaut in the command module would have been at least 3500 km from any other human.
There are enough inhabited islands in the oceans that it is hard to find a place where you might be 3500 km from anybody. For example, draw a 3500 km circle centered on Hawaii and that takes care of a pretty big chunk of the middle of the Pacific.
Get out of that circle, and you are now close enough to the US, Japan, and New Guinea to have someone within 3500 km.
Southeast prospects are better, but before you get 3500 km from Hawaii, you are within 3500 km of the Pitcairn Islands.
It does look like there might be places in the ocean that are 3500 km from any inhabited place, but then you have to add in 3500 km circles around every ship and every plane (well, slightly smaller for the planes as they are at high altitude). That is going to take a lot out.
And don't forget the International Space Station! If could be over 3000 km from the point it is directly over, and you'd be within 3500 km of it.
The ISS orbits between 330km and 410km above the earth. Really just a hair's breadth off the planet, skimming the outside of the atmosphere.
While distance is one measure of loneliness, travel time would be another.
I'd suspect among the most isolated humans were early Antarctic explorers. Robert Scott, when he died on the return leg of his failed South Pole expedition, was some 400 miles (670 km) from his intended destination. Very few McDonalds' in the neighborhood, I'd wager.
There are enough inhabited islands in the oceans that it is hard to find a place where you might be 3500 km from anybody. For example, draw a 3500 km circle centered on Hawaii and that takes care of a pretty big chunk of the middle of the Pacific.
Get out of that circle, and you are now close enough to the US, Japan, and New Guinea to have someone within 3500 km.
Southeast prospects are better, but before you get 3500 km from Hawaii, you are within 3500 km of the Pitcairn Islands.
It does look like there might be places in the ocean that are 3500 km from any inhabited place, but then you have to add in 3500 km circles around every ship and every plane (well, slightly smaller for the planes as they are at high altitude). That is going to take a lot out.
And don't forget the International Space Station! If could be over 3000 km from the point it is directly over, and you'd be within 3500 km of it.