We study thermodynamic and structural properties of a Lennard-Jones liquid at a state very close to the triple point as the radius of a hard sphere solute is varied. Oscillatory profiles arise for small, molecular sized radii while for large radii smooth interfaces with a ``drying layer'' of low vapor density near the solute are seen. We develop a quantitative theory for this process using a new mean field treatment where the effects of attractive interactions are described in terms of a self-consistently chosen effective single particle field. We modify the usual simple molecular field approximation for the effective field in a very natural way so that exact results (consistent with a given accurate equation of state for the uniform fluid) arise in the ``hydrostatic limit'' of very slowly varying interfaces. Very good agreement with the results of computer simulations for a wide range of solute radii are found.