The effect of the near-field distribution of sharply etched, nanometer-sized gold tapers on angle-resolved kinetic energy spectra of electrons photoemitted by ultrafast laser pulse irradiation is investigated both experimentally and theoretically. In the experiments, the enhancement of the local electric field at the tip apex is sufficiently large to enable optical field induced tunneling of electrons tunnel out of the metal tip. Strong field gradients near the tip apex, with a decay length shorter than the quiver amplitude, accelerate the electrons to high energies within less than one optical cycle. This electron emission is confined to a narrow cone angle around the taper axis, while low-energy quiver electrons cover a much broader angular range. This sub-cycle acceleration manifestly alters the energy distribution of the emitted electrons, resulting in pronounced plateaus in their kinetic energy spectra. The electron motion in the curved vectorial electric field is analyzed and it is shown that observed changes of both the kinetic energy spectra and their angular distribution depend sensitively on the near-field decay length and curvature, which indicates that such angle-resolved kinetic energy spectra of photoemitted electrons give information on the optical near-field distribution in the vicinity of nanometer-sized field emitters.