The solvation properties of ions in aqueous solution are determined by the unique structure of water and its dielectric properties. The orientational structure of the water molecules is governed in part by the dipolar nature of water but displays a much richer behavior due to hydrogen bonding. Here, properties of the orientation angle theta of a water dipole as a function of distance r from the ion, namely, the mean value [cos theta](r) and the distribution P(cos theta;r), are calculated from molecular dynamics simulations of Cl- in water. The orientational behavior is compared to that of a point charge and a point dipole in a dielectric continuum, which can be solved analytically. More specifically, the microscopic field due to a point charge experienced by the dipole is different than the macroscopic field due to a point charge so that the problem must be viewed as a dipole in a cavity immersed in a dielectric continuum, using arguments similar to those of Kirkwood in relating the dielectric constant epsilon of a fluid to the dipole moment mu of molecules in the fluid. By comparing (cos theta)(r) calculated from simulation with the analytic expressions, an apparent "local" dielectric response epsilon(r) dependent on r is calculated; epsilon(r) is termed apparent because it is not a position-dependent dielectric constant to be used in the Poisson or Poisson-Boltzmann equations but rather reflects the cumulative effects of such a position-dependent dielectric constant.