In this work, ion partitioning and selectivity in cylindrical nanopores with heterogeneous surface charges at equilibrium with reservoirs are investigated by a two-dimensional (2D) classical density functional theory (DFT). We present an efficient numerical method for the large 2D system in which the fast Hankel transform and fast Fourier transform are used to calculate convolution integrals, and a hybrid method of Picard iteration and Anderson mixing is used to solve the Euler-Lagrange equations. The performance of the 2D DFT is tested by calculating the profiles of a model electrolyte in long homogeneous cylindrical nanopores. The profiles from the 2D DFT model matches well with those from a 1D DFT, and the computing time of the hybrid iteration algorithm is six times shorter than that of pure Picard iteration. We apply the model to electrolytes in cylindrical nanopores with heterogeneous surface charges. It is found that the ion adsorption and selectivity are strongly affected by the surface charge pattern, the magnitude of the surface charge, the size of charged domains on the surface, and the pore size.