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We report two-dimensional localization of exciton polaritons in a coherently pumped planar semiconductor microcavity operating in the strong-coupling regime. Two-dimensional polariton solitons exist despite the opposite dispersion signs along the orthogonal in plane directions. Nonlinearities compensating the opposing dispersions have different physical origins and are due to the repulsion of polaritons on one side and due to parametric four-wave mixing on the other. Both of these nonlinearities can support their respective families of one-dimensional solitons, which coexist with each other and with the two-dimensional solitons.