Hexagonal honeycombs and their use in composite structures has become commonplace in aerospace design and other fields. Polymer-filled honeycomb structures, where the hexagonal cells are filled with an elastomer, are of interest for their ability to increase the stiffness of the composite over that of the elastomer or honeycomb individually. Previous research by the authors has demonstrated that the effective behavior of such composites is determined by both the honeycomb geometry as well as the material properties of the infill and cell wall. Infill stiffness amplifications of over three orders of magnitude have been predicted, which could be an attractive option for improving the performance of smart materials such as shape memory polymers. Considering the benefits of such composites, it is of interest to optimize the honeycomb cell geometry to maximize the stiffness increase observed in the infill material. To meet this objective, in this work a unit cell finite element model was created for a hexagonal, thin walled honeycomb. Six design variables describing the honeycomb geometry were selected, and parametric studies of these design variables in the objective have been generated. Informed by these studies, an estimation of the Pareto front has been completed, with chosen objectives of the maximum composite in-plane modulus and modulus ratio, in one material direction. Promising designs are identified, and the range of effective composite properties if discussed. While this problem considers fixed infill properties, the methods applied could readily be extended to smart material infills. The contour plots and performance estimation employed in this research provides an important step in the design of improved smart composites for use in morphing and variable stiffness structures.