The thermodynamic stability of NaI salt ion pairs in water clusters has been investigated by means of ion pair potential of mean force calculations employing Monte Carlo simulations with model potentials and free energy perturbation theory. In the simulations the ion pair is described by semiempirical valence-bond theory, while the water model potentials employed include the standard liquid-phase TIP4P/OPLS and a polarizable five-site water model that we have developed for cluster simulations. The latter model is parameterized in order to reproduce small cluster experimental data supplemented by ab initio MP2 calculations with a modified 6-31+G** basis (and pseudopotentials for iodine). Simulations with both models yield similar qualitative features for the cluster ion pair potentials of mean force and resulting cluster equilibrium constants, even though they exhibit some quantitative differences. A major finding of our theoretical study is that the ion pair is quite stable with respect to dissociation into free ions, even in very large clusters, and an analysis of cluster solvation energies with a simple dielectric model suggests that the stability of the ion pairs is in fact related to the very slow convergence of cluster ion solvation energies with increasing cluster size, which makes separated cluster ions thermodynamically unlikely. Rather, the ion pairs tend to exist as "contact" ion pairs and solvent-separated ion pairs in the larger clusters, a feature which is likely to be overemphasized in simulations with the TIP4P/OPLS model potentials, which illustrates the importance of solvent-solvent and solute-solvent polarization in model potentials. Preliminary ab initio characterization of model cluster excited states suggests that NaI(H2O)(n) cluster "contact" ion pairs have optically accessible excited states akin to that of gas-phase NaI, hence making photodissociation experiments feasible, but that electronic transition oscillator strengths significantly decrease for model solvent-separated ion pairs. As a result, the larger cluster ion pairs, which are mainly solvent-separated, will not be involved in cluster photodissociation reactions via a mechanism akin to gas-phase NaI photodissociation, in agreement with recent experimental findings.