"Some are actually easier to reach than the Moon, they're easier to land on and
take off from, and they will do nicely for mining purposes.

Then the Moon, then Mars, then the rest of the Sol system, then the Milky Way galaxy,
then the rest of the Universe, then all the other universes in the Metaverse.

Besides, we've got an NEO just 7 million miles away with two moons!"

But it isn't always just 7 million miles away.
Besides that, it isn't a matter of distance but rather a matter of Delta-v and distance.
As far as I'm aware the Moon is easier to get to than compared to any NEO. And unlike the Moon, no NEO is less than a week away. The Moon is always about 1 1/2 light seconds from Earth.
If we had a space rock in the Earth's L points, that would be a different matter. But we don't.

Of course one thing you might do is move a space rock to a Earth L point, nice safe size rock, say around 60' in diameter. Such a rock if say it had 25% water could have over 1000 tons of water and thousands of tons of other minable material. If water is selling for $500-1000 per lb, it's 1-2 billion dollars worth of water.

Another aspect about NEOs is they could function as way stations/cyclers such as for the journeys to Mars.

NEOs would be my second option if the Moon doesn't have minable water- because I think it's in NASA's interest and anyone interested in opening up the space frontier [which should include everyone on Earth] to find minable water in the space environment.

Another aspect about this is, we talking about the goals of a space agency- rather than say some space mining company. It could make sense for a space company to "improve" a space rock [move it to better location for example], and thereby claim the rock and it's mineral rights. Now, such an idea has legal problems, but perhaps these problems can be overcome- btw, the Moon and Mars also has similar legal problems in regard to claiming mineral rights.

But as I said we are talking about the direction of a Space agency. And involving this nation in the development of the Moon and Mars could have certain advantages in terms of long term national goals.
Our goal should be develop markets in space- rocket fuel in space being a important first market [which also involves starting energy market in space, etc]. If one could buy rocket fuel on the lunar surface, getting to the Moon and back is easier. If you extend this to having rocket fuel that one can buy at LEO, and High earth orbit/lunar orbit, getting to the Moon became almost a cake walkish. And the Moon can be transformed into the Earth's spaceport.

The Moon and Mars are destinations. Such as for the general public- such as tourists. And one have research, retirement, storage and other things. In other words, the Moon and Mars are places in which humans can colonize.

And if we get to the point of McDonalds on the Moon, then we will be without any doubt mining lots of NEOs and doing a lot of other things.