  Several material families show competition between superconductivity and
other orders. When such competition is driven by doping, it invariably involves
spatial inhomogeneities which can seed competing orders. We study
impurity-induced charge order in the attractive Hubbard model, a prototypical
model for competition between superconductivity and charge density wave order.
We show that a single impurity induces a charge-ordered texture over a length
scale set by the energy cost of the competing phase. Our results are consistent
with a strong-coupling field theory proposed earlier in which superconducting
and charge order parameters form components of an $SO(3)$ vector field. To
discuss the effects of multiple impurities, we focus on two cases: correlated
and random distributions. In the correlated case, the CDW puddles around each
impurity overlap coherently leading to a `supersolid' phase with coexisting
pairing and charge order. In contrast, a random distribution of impurities does
not lead to coherent CDW formation. We argue that the energy lowering from
coherent ordering can have a feedback effect, driving correlations between
impurities. This can be understood as arising from an RKKY-like interaction,
mediated by impurity textures. We discuss implications for charge order in the
cuprates and doped CDW materials such as NbSe$_2$.
