A comprehensive systems code that includes a range of physics and engineering considerations along with a simplified costing model has been utilized to evaluate the primary cost drivers for a compact tokamak pilot plant. The systems code has been benchmarked against several tokamak reactor designs and is utilized with sophisticated optimization algorithms to develop optimal solutions for a set of user-specified assumptions and design constraints. In contrast to previous models that have focused on the cost of electricity as the key cost metric, this study uses the estimated capital cost of the facility. The analysis suggests that a pilot plant with the following features may offer potential for a cost-attractive pilot plant: A ~ 3, H98y2 > 1.5, Pnet = 200 MW,  ~ 1 to 2 h utilizing rare-earth barium copper oxide (REBCO) magnet technology and a plug-bucked central solenoid/toroidal field (CS/TF) magnet support structure. While REBCO magnets offer some advantages relative to Nb3Sn magnets in all cases, the most gain is obtained when combined with the plug-bucked CS/TF bucking solution. Pulsed operation reduces capital cost requirements relative to steady-state operation, especially at low confinement. Cost sensitivity studies indicate that there are significant cost uncertainties associated with the achievable confinement quality, tritium breeding capability, attainable thermal efficiency, and achievable neutron wall loading, suggesting that these areas are the most critical areas in reducing the cost risk for a compact tokamak pilot plant. Further cost sensitivity studies indicate that the estimated cost is most sensitive to the underlying cost of the magnetic coils, providing further impetus to better establish cost-effective means for producing fusion magnets.