The goal of further reducing the Levelized Cost of Energy (LCOE) has driven the investigation of large-scale wind turbines. This work presents a simple, rapid and detailed approach for the structural design of the tower and monopile without a controller, but with frequency and high fidelity structural verification. The approach uses an optimization to reduce the mass of the structures while meeting strength, buckling and geometric constraints by using analytical equations. A verification of frequency constraints is performed with BModes, and ANSYS Mechanical APDL is used for high fidelity verification of stress and buckling. The approach is applied to study the design space of three 25 MW offshore wind turbines with different rotor diameters and cone angles, and to evaluate the nacelle center of mass fore-aft location effect. Results obtained show that the tower and monopile are more susceptible to changes in the rotor thrust than the overturning moment even for designs with high pre-cone angle and large distance of the nacelle center of mass from the tower axis. But it is possible to obtain structurally feasible tower and monopile designs for the three 25 MW turbines studied while not exceeding diameter and wall thickness limits. However, mass penalties can be decreased by 0.8-14%, to further reduce the cost of energy, by increasing the diameter limit which may require manufacturing technology development. The approach applied and studies serve to understand the design space of the tower and monopile for a 25 MW turbine, and provide baseline designs that can be used in the development of a controller and evaluation of a full suite of design load cases.