Many, perhaps most, asteroids are large enough to have their own gravity, although it's not what we're used to. At least it would allow proberly designed pumps and things to operate, and the dust would settle ... eventually.
Someplace out there is going to become a sort of hub. Maybe it will be Ceres, or Vesta, but it will probably be one of the big ones.
A slick trick will be to find one that is rotating slowly, and tether your spacecraft to it. As the asteroid rotates, it will provide artificial gravity to you while you are sleeping, and keep your bones strong, but when you are working on it, you will be able to lift ten-ton boulders.
Don't drop them on your foot, though.