We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava?s gravity. For any value of the Hořava parameter omega, there are values of the gravitational mass M for which the metric describes a naked singularity, and this isalways accompanied by a vacuum ?antigravity sphere? on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to tho