Near-Earth Asteroid 4660 Nereus has been identified as a potential spacecraft target since its 1982 discovery because of the low delta-V required for a spacecraft rendezvous. However, surprisingly little is known about its physical characteristics. Here we report Arecibo (S-band, 2380-MHz, 13-cm) and Goldstone (X-band, 8560-MHz, 3.5-cm) radar observations of Nereus during its 2002 close approach. Analysis of an extensive dataset of delay-Doppler images and continuous wave (CW) spectra yields a model that resembles an ellipsoid with principal axis dimensions X=510±20 m, Y=330±20 m and Z=241-10+80 m. The pole direction is approximately located at ecliptic pole longitude and latitude of λ=+25°, β=+80° with the uncertainty radius of 10°. Our modeling yields a refined rotation period of 15.16±0.04 h. Nereus has a circular polarization (SC/OC) ratio of 0.74±0.08, which implies substantial near-surface centimeter-to-decimeter scale roughness. Dynamical analysis of our model suggests that YORP alteration of the rotation period may become evident within a few years. Nereus has two stable synchronous orbits where natural material may remain in orbit, while most asteroids observed to date do not have such stable synchronous orbits. We also find that spacecraft orbits about Nereus are feasible.