I was 8 when Armstrong and Aldrin set foot on the moon. It was exciting. My daughter is 18 and has never witnessed anything of the same order of excitement. The human genome project was comparable in some ways but lacked the buzz. Ha ha!
There is excitement about going back now. We will, and on to Mars. We can do space so much more safely now than back in the 60s. Commercial companies are pioneering space tourism and later on will pioneer the mining bits. But the excitement recently is over the space elevator. The idea is that a cable can stretch all the way from the surface out into space, balanced by gravity, and used as a means to cart stuff back and forth instead of having to use rockets, making it easier, less expensive and less dangerous.
It will happen eventually on Earth. We need to make new materials that are strong enough. Carbon nanotube cables and other fancy materials will be needed that we can’t make long and strong enough yet. But the moon has lower gravity so it is much easier there and will likely happen earlier.
Nextbigfuture has a nice summary: http://nextbigfuture.com/2012/08/unlike-earth-space-elevators-lunar.html and the NASA document is at http://www.spaceelevator.com/docs/iac-2004/iac-04-iaa.3.8.3.07.pearson.pdf
So I don’t need to repeat everything here. Instead, I am wondering about applying a derivative of my idea for a 30km tall building: http://nvireuk.com/2012/02/12/super-tall-30km-carbon-structures/
A 30km tall building on Earth could make use of atmospheric buoyancy for the lower end, which of course we wouldn’t get on the moon. But we also wouldn’t get wind on the moon to add stresses. And on the moon gravity is less so the structure could be much taller. On the moon a graphene structure could form as much as the bottom 150-200km of the climb. It might offer a nice synergy. Or perhaps it is just easier to add 200km to the elevator cable. I don’t know, and no longer have the maths ability to calculate it. Maybe worth a look though.