Atomistic simulations of a simple Lennard-Jones fluid are used to investigate the very near-wall dynamics and thermodynamics of evaporating menisci. The specific configuration considered is a two-dimensional (in the mean) liquid drop centered on a cold spot on an atomically smooth solid wall with evaporating menisci extending from it onto hotter regions of the wall. In the four cases simulated, the interaction energy between the solid atoms, which make up the wall, and the fluid atoms, which are equilibrated in liquid and vapor phases, is varied by a factor of about 5. Results are interpreted in the context of a recently proposed continuum model [V. S. Ajaev and G. M. Homsy, “Steady vapor bubbles in rectangular microchannels,” J. Colloid. Interface Sci. 240, 259 (2001)], which is based on a low-capillary-number asymptotic analysis of the flow and heat equations. In this model, the nonlocal influence of the wall is modeled by a disjoining pressure, a common linearized nonequilibrium model is assumed for evaporation kinetics, and the interface curvature impacts thermodynamics through its effect on the local pressure. However, this model and others like it neglect both the atomic granularity of the fluid and any scale associated changes in its properties in the thinnest regions of the evaporating meniscus, which are the subject of this study. Quantitative agreement for meniscus shape and evaporative mass flux is found for a weakly wetting case, but the model must be modified in a straightforward way for more strongly wetting cases to account for a layer of nearly fixed fluid atoms on the wall. A finite solid-liquid interface thermal (Kapitza) resistance is found to be important, and the continuum model is reformulated accordingly. With an appropriate Kapitza resistance value the reformulation yields accurate predictions using the actual wall temperature as a boundary condition, rather than the fluid’s temperature at the wall.