The surface spin polarization in the epitaxial films of a prototype manganite, La0.7Sr0.3MnO3, has been investigated by Scanning Tunneling Spectroscopy with ferromagnetic SP tips at room temperature. The manganite surface splits into ferromagnetic (FM) and paramagnetic(PM) regions characterized by metallic and insulating like behavior respectively. Spin polarized spectroscopy with Ni tips has been performed separately for the two phases, and the results compared with standard W and Pt tips. While PM exhibits featureless tunneling characteristics, the FM regions exhibit at room temperature strongly nonlinear behavior with a band-gap like behavior. The spin resolved density of states of the FM regions of the manganite has been extracted by the deconvolution of the spectroscopic curves. It indicates very high spin polarization (nearly halfmetallic behavior) with the spin down band separated from Fermi level by 0.4 eV. This value corresponds exactly to the gap value measured for the whole surface of this manganite at low temperatures. Thus the surface of the La0.7Sr0.3MnO3 films maintain even at room temperature nano- and micrometric islands of very high spin polarization, while the total polarization is given by the coverage of the surface by FM regions. This result is extremely important for spintronic applications of this material and indicates possible roots for the realization of manganite nanosized devices with extremely high spin polarization.