This paper addresses two-dimensional direction-finding using one-bit quantized signals to reduce hardware cost and computational complexity while maintaining accurate direction-of-arrival (DOA) estimation. The performance of different array geometries is investigated and compared, including the uniform circular array (UCA) and the three-sided linear array. A novel sparse circular hybrid array is proposed; its architecture consists of a UCA with two additional elements extended along the z-axis, which significantly enhances the accuracy of azimuth and elevation estimation. Mutual coupling effects are modeled using experimentally measured coupling matrices and compensated through the MUSIC algorithm by incorporating algorithmic correction techniques and electromagnetic design strategies. Simulation results (SNR=10dB) indicate that these compensation methods reduce azimuth estimation error to 0/01° across the UCA, three-sided linear array, and proposed array, while elevation estimation error improves to 0/04° for the UCA, approximately 0/009° for the proposed hybrid array, and 0/16° for the three-sided linear array. Overall, the proposed sparse circular array combined with the MUSIC algorithm improves localization accuracy while reducing system design costs and computational complexity.