Any major manned project at this point is going to involve a lot of robotic probes and preparation.
Yeah, we're already doing that. We've sent robotic probes to the Moon, Mars, and the asteroid belt lately. Have you forgotten about all the hubbub over the bright spots they found on Ceres? We are *not* ignoring the asteroid belt.
But asteroids are a lot easier to get to and from than Mars, precisely because of their lack of gravity and lack of atmosphere.
I disagree. True, Mars has enough of an atmosphere to be a nuisance (because you need reentry shielding, but there's not enough there to be really useful for aerobraking), but it's also significantly closer than the belt. Farther = a longer journey. For a probe, a few extra months might not be that big a deal, but for humans, it is. Mars is already too far as it is (as in, "too long a journey for most people to want to sit in a spacecraft that long", plus the radiation concerns).
A lunar space elevator might be a nice project. But in the end, the moon is a really harsh environment, the resources it has are hard to get at, and it, too, has just too much gravity.
The environment isn't that harsh; it's 3 days away (super-close in celestial terms), and there's no annoying atmosphere, and just enough gravity so that we can operate on it without having to invent all-new methods for every simple little thing. But the gravity is low enough that a lunar space elevator should be quite doable, unlike Earth (where the gravity is way too high so we don't have good materials with enough strength, and we have a thick atmosphere that causes all kinds of problems with such an elevator).
The proximity of moon to earth also means that remotely operated robots are a reasonable alternative to manned exploration.
I disagree entirely. For simple probing around, sure, that'll work OK, but if you want to do any really serious work, you have to have boots on the ground. Remotely-operated vehicles are *not* going to build factories, mines, etc. We do *not* have that kind of technology yet. Some heavy-equipment stuff could definitely be converted to remote-control: dump trucks, shovels, etc. But that'll only work as long as nothing goes wrong. As soon as something breaks or gets stuck, you're going to need some people there to deal with it. So you could definitely get by with a lot less manpower on-site, by operating a lot of vehicles remotely, but you'll still need some. It's just like our UAVs ("drones") used by the US military: the planes are flown remotely, I think even by people stateside, but you still have to have real people on-site in the theater to refuel them, do maintenance work, etc., when they land. It'll be the same for heavy equipment on the Moon.
I still think our primary focus should be exploration of the asteroid belt, first with robotic probes, then towing asteroids into lunar orbits, creating habitats, and finally moving out there.
We're already exploring the asteroid belt. We could stand to do more though. But there's no reason we can't get started building habitats and industrial facilities on the Moon simultaneously. We already know there's a crapload of asteroids out there with valuable ores, so we might as well prepare for using them. And we should definitely be working right away on building the technology for capturing and towing these asteroids.