During the 60's the cold war was at its peak and the domination of near earth space was one of the primary focus of both the US and the USSR. To go to the moon before the end of the 60's, with the technology of that time, was probably the biggest and most risky achievement of the 20th century (and probably one of the biggest in human history in general). But the economical, social and political forces that drove this achievement slowly decayed in the following years / decades. And that was to be expected. The cold war brought USSR to each knees, financially and socially and eventually its dissolution. But it also brought the US space program to a halt as it lost focus. This back and forth continuous change of policy brought by every new president is the main reason why we are still in LEO.
But it seems that things are changing: Space-X, and other private companies, is making steady progression and we are very close to see the US return to manned space flight. Now how long it will take for humans to return to the moon and eventually go to Mars I don't know. I believe the moon is the next logical step and a wise decision by Trump administration. It is close(r) to the earth and if something goes wrong it can be reached and return from more easily compared to Mars.
As for the timeline I think it will take at least 10 years to set an orbital outpost to the moon and another 10-15 to Mars.
I've been dismayed in all this time, the furthest our crewed missions have gone to is the moon, we really haven't done any better in that respect since the 60s. Asimov mentioned human inertia, and the only way to get people to do something is to make them face a serious threat to their existence. In his series, it required the intentional radiation poisoning of the entire surface of the Earth to make people leave the planet and colonize space.